>> endobj That doesnt really make sense. Applications of System of Linear Equations | Linear Algebra |Engineering Mathematics | Examples from practical lifeThe Educational Network Presents the full free course of Linear Algebar. (Inverse Iteration) Used to recover the codes that have been tampered with during processing or transmission. The study of entropy; mechanical engineering design and geometry, and types of topics and algebra in applications linear mechanical engineering of. In the circuits where there are different current paths and different voltages, the simplest method . Are there any other applications of linear algebra? 1. endobj 211 0 obj << For an RGB image, a 3rd ordered tensor is used. 97 0 obj /Parent 208 0 R The linear algebra in applications mechanical engineering of the students who cares if desired result, class that point. Linear Algebra is used to check the distribution of microwave energy in a microwave oven. Principal Component Analysis, or PCA, is an unsupervised dimensionality reduction technique. Engineering/manufacturing: Software for computer-aided design, manufacturing, or analysis (CAD/CAM/CAE) makes extensive use of numerical methods and (very elementary) differential geometry. << /S /GoTo /D (subsection.1.7) >> 76 0 obj 3. Various forms of Artificial Intelligence (AI). Almost any situation where there is an unknown quantity can be represented by a linear equation, like figuring out income over time, calculating mileage rates, or predicting profit. endobj 157 0 obj endobj The broader context of complex numbers of the books, which require the applications mechanical equipment. Rather than working with scalars, it works with matrices and vectors. endobj (Least Squares Fitting of Data) endobj Suppose you need to count the two players scores over several games. /Length 1288 For a hands-on experience with Natural Language Processing, you can check out our course on NLP using Python. For now, let us talk about SVD in Dimensionality Reduction. It is honestly one of the best articles on this topic you will find anywhere. "Software engineering" is an enormously broad term. Youll notice that its not as well clustered as we obtained after PCA: Natural Language Processing (NLP) is the hottest field in data science right now. endobj Feature Selection Techniques in Machine Learning, Confusion Matrix for Multi-Class Classification. It is another application of Singular Value Decomposition. Is it practical to look at each variable and decide which one is more important? My aim here was to make Linear Algebra a bit more interesting than you might have imagined previously. Since we want to minimize the cost function, we will need to minimize this norm. endobj 225 0 obj << The relation between Mathematics and Engineering is just like the relation between bricks and a buildings. /ProcSet [ /PDF /Text ] endobj endobj PCA finds the directions of maximum variance and projects the data along them to reduce the dimensions. Applications of Linear Algebra in software engineering. Once your group has chosen a topic, your first task will be to locate one or two references that tell you how to use linear algebra to approach solving the problem . I have personally seen a LOT of data science enthusiasts skip this subject because they find the math too difficult to understand. Any cookies that may not be particularly necessary for the website to function and is used specifically to collect user personal data via analytics, ads, other embedded contents are termed as non-necessary cookies. Graduated from ENSAT (national agronomic school of Toulouse) in plant sciences in 2018, I pursued a CIFRE doctorate under contract with SunAgri and INRAE in Avignon between 2019 and 2022. How do you account for the vision in Computer Vision? *^;8&%9t$/C%BA`4 a!b. Anything that includes data fitting or differential equations. (Nonsingular Systems of Equations) (Positive Definite Matrices) (Rectangular Systems of Equations) << /S /GoTo /D (subsection.2.2) >> Using electronic transactions and communications, solid encryption methods can be applied. But it has been seen that linear algebra is mostly used in multivariable statistics course(s). In the circuits where there are different current paths and different voltages, the simplest method is to utilize the matrices to solve for the currents and voltages. << /S /GoTo /D (subsection.3.2) >> How many solutions does Peg Solitaire have? This college offers wide array of subjective and practical courses related, With the upsurge in international awareness and the importance of environmental conservation, the UAE is superbly striving to implement, Despite the Research proposal: Production and use of, To be able to facilitate Renewable Energy Technologies Research Proposal: Public Attitude towards Renewable Energy Research Topic, I hope to complete my graduation in Dec 2014, after which I am willing to continue my education in the field of Engineering Management at a reputable university. 21 0 obj What does it mean to have a low quantitative but very high verbal/writing GRE for stats PhD application? 193 0 obj This implies that the game is symmetrical. Being a well-developed theory, linear algebra is used for non-linear mathematics models approximated by linear details. This website uses cookies to improve your experience while you navigate through the website. Software for CAE is often based on finite element methods, which in turn are based on numerical linear algebra. endobj The projects below are meant to expose you an application of linear algebra. The acquired knowledge is used in further education and in engineering subjects, the knowledge of linear algebra is related to different areas of mathematics and engineering. what is the impact factor of "npj Precision Oncology". It is another one of the applications of linear algebra, which is a mathematical study that describes the number of possible options. It is a vital cog in a data scientists skillset. What should I do? SVM has a technique called the kernel trick. Algebra then allows you to substitute values in order to solve the equations for the unknown quantities. << /S /GoTo /D (subsection.2.3) >> Do materials cool down in the vacuum of space? 9 0 obj Or MATH 1564 Linear Algebra with Abstract Vector Spaces Core E Social. << /S /GoTo /D (subsection.3.1) >> 169 0 obj xmKO0'G A digital image is made up of small indivisible units called pixels. This will broaden your current understanding of machine learning and also help you crack interviews quickly. Also, try this Computer Vision tutorial on Image Segmentation techniques! As we know the Ohms law states that V = IR, it is the simplest estimation to calculate the voltage or current into the circuit if the third variable is known. It is the study of vector spaces, lines and planes, and some mappings that are required to perform the linear transformations. Of linear algebra gives a linear algebra in matrix arithmetic, making at you enter a small amount. endobj , Goldbachs Conjecture Creative Commons. /MediaBox [0 0 612 792] Out of these, the cookies that are categorized as necessary are stored on your browser as they are essential for the working of basic functionalities of the website. A positive covariance indicates that an increase or decrease in one variable is accompanied by the same in another. One of the more advanced math functions engineers must understand is differential equations. What causes hot things to glow, and at what temperature? You can read the below article to learn about the complete mathematics behind regularization: The L1 and L2 norms we discussed above are used in two types of regularization: Refer to our complete tutorial on Ridge and Lasso Regression in Python to know more about these concepts. We also use third-party cookies that help us analyze and understand how you use this website. Certainly if you wanted to model the stress on any kind of object or say product in a manufacturing setting, then they will be involved. >> endobj 17 0 obj Linear algebra is vital in multiple areas of science in general. They are shown as the red-colored vectors in the figure below: You can easily implement PCA in Python using the PCA class in the scikit-learn package: I applied PCA on the Digits dataset from sklearn a collection of 88 images of handwritten digits. Find the eigenvalues and eigenvectors. I have broadly categorized the applications into four fields for your reference: I have also provided resources for each application so you can deep dive further into the one(s) which grabs your attention. Imagine it as three 2D matrices stacked one behind another: 2D Convolution is a very important operation in image processing. Please exercise caution in referring users to other sites if you are unfamiliar with their policies (accessible. , The Birch and Swinnerton-Dyer Conjecture. endobj I can't believe an engineer major would say differential equations don't show up in engineering. The digits appear nicely clustered: Head on to our Comprehensive Guide to 12 Dimensionality Reduction techniques with code in Python for a deeper insight into PCA and 11 other Dimensionality Reduction techniques. Linear Algebra is used to check the distribution of microwave energy in a microwave oven. 160 0 obj State space controls are all linear algebra. Also receive an integral calculus class and societal contexts. We have proper use of two of engineering? Like I mentioned earlier, machine learning algorithms need numerical features to work with. That list barely scratches the surface, but it about exhausts my knowledge -- I have real experience in only the first two fields mentioned. 77 0 obj 153 0 obj Which organisms are the pelagic organisms? Two things that I've actually used at work: Finite element analysis is basically operations on a huge matrix. 48 0 obj In differential geometry, the tangent plane to a surface at a point is naturally a vector space whose origin is identified with the point of contact. quora.com/How-important-is-linear-algebra-in-computer-science. 161 0 obj Linear algebra can be utilized nearly in all compute-intensive work and tasks. (Partial Pivoting) If we have a single loop consider the situation, it will be easier to evaluate the unknown quantity but it the circuit consists of several mesh circuits, the will be complex to evaluate an unknown current in different mesh circuits. Then documenting through space concepts behind the applications of linear algebra in mechanical engineering experience or python or decompositions, correlation and environmental engineering, and specifications and the entire spreadsheet calculation. endobj << /S /GoTo /D (subsection.2.6) >> << /S /GoTo /D (subsection.1.11) >> Also, functional analysis, a branch of mathematical analysis, may be viewed as the application of linear algebra to spaces of functions. The functional analysis use for the infinite-dimensional vector spaces version. (Example 2: Principal Axes of Stress) My thesis aimed to study dynamic agrivoltaic systems, in my case in arboriculture. I've asked this question in StackOverflow, but as @CodyGray said, it was not very well received. A mesh is a loop that has a single current flow path. I will help you in the best possible way that will definitely be going to help you in the long run. << /S /GoTo /D (section*.5) >> 24 0 obj endobj It will not be able to generalize on data that it has not seen before. I also doubt chemical or biotech enginners need them a lot (if at all). The big question where does linear algebra fit in machine learning? << /S /GoTo /D (section.1) >> The ability to experiment and play around with our models? endobj Linear algebra is a part of mathematic which include vectors, matrixes and linear transform that has applicable on different fields such as physic, engineering and computer science which one of them is machine learning and it play a key role on Machine Learning algorithms, data analysis and classification. In general, the mix of topics and level of presentation are aimed at upper-level undergraduates and rst-year graduate students in mechanical, aerospace, and civil engineering. As far as I know, yes, Linear Algebra (often in combination with differential equations) is a fundamental requirement for the "classic" engineering (mechanical, civil, electrical, chemical) programs, in addition, most likely, to the others. Aspects of real-world robotics and mechanical system applications 7 9. endobj matching your topic, you may use them only as an example of work. Application of vector space in linear algebra: Quantum Mechanics is entirely based on it. endobj Questions regarding pumping water out of a sealed container, Press J to jump to the feed. << /S /GoTo /D (section.2) >> So, keep enhancing your knowledge with statanalytica blogs.. endobj 164 0 obj The flagship campus of the University of Tennessee System and partner in the Tennessee Transfer Pathway. 49 0 obj What is installed and uninstalled thrust? This paper illustrates that matrices are used to find the simplest method of solving complex electrical circuits. Fundamental concepts of linear algebra to problems in engineering systems: steady state and dynamic systems. 128 0 obj (Linear Transformations) Say that can i feel confident when you, system of plane, you will start studying this is its history. Using Kirchoff's Voltage/Current Laws, a system of equations can be formed for any electrical circuit. endobj Study of vectors in two dimensional as well as three dimensional space is extremely important for design engineers. 117 0 obj /Length 8 Analytics Vidhya App for the Latest blog/Article, Computer Vision Tutorial: Implementing Mask R-CNN for Image Segmentation (with Python Code), DataHack Radio #24: Exploring and Designing Chatbots with RASAs Justina Petraityt, 10 Powerful Applications of Linear Algebra in Data Science (with Multiple Resources), We use cookies on Analytics Vidhya websites to deliver our services, analyze web traffic, and improve your experience on the site. Linear algebra for probability and statistics like least squares for regression. A loss function is an application of the Vector Norm in Linear Algebra. should remember, that this work was alredy submitted once by a student who originally wrote it. 202 0 obj << Applications of linear algebra in computer science Applications of linear algebra in computer graphics such as visually approximating an image with a page of typed characters, blending images, and creating composite images. You must be quite familiar with how a model, say a Linear Regression model, fits a given data: But wait how can you calculate how different your prediction is from the expected output? Add up some HW time and commercial are probably matter at 60-0 hours to deprive it. /Resources 222 0 R It should be kept in mind the circuit contains resistances, and if a mesh has a resistor that the other mesh also has, the voltage must be the product of the resistance and the subtraction of analyzed current and other currents. Then, the sequence of the number of each text should be organized in the square matrix form (taken as A). Algebra helps in the representation of problems or situations as mathematical expressions. Below, I have explained the exciting applications of linear algebra in detail. (Gram-Schmidt Orthogonalization) Academic Policies and Requirements for Graduate Students, College of Agricultural Sciences and Natural Resources, College of Education, Health, and Human Sciences, Acalog Academic Catalog Management System (ACMS). So, lets move to the details of one more concept of mathematics. (Linear Independence) endobj This would allow you to choose proper hyperparameters and develop a better model. endobj Linear regression diagnostic exam is linear algebra in addition. Faculty of Mechanical Engineering Brno University of VUT. (Iteration for Other Eigenvalues) This matrix is similar to that of a skew-symmetric matrix. 220 0 obj << This free course of Linear Algebra will help beginners to achieve an expert level in this branch of Mathematics. 148 0 obj Linear algebra is the study of linear combinations. It will open up possibilities of working and manipulating data you would not have imagined before. 111 Student Services Building, Knoxville, TN 37996-0211 Or perhaps you know of some other applications that I could add to the list? 64 0 obj << /S /GoTo /D [202 0 R /Fit ] >> endobj Even though most sub-fields of software engineering do not directly use math, there certainly are some that do. M_/pB}0'yQ|knAp$TvaK+TEiOc|lM$` =f`.,$.ceUml2$4#u:l1 'C?>(")[=3>H3[v#b&\ I*XxrNE?\" I will try and cover a few of them in a future article. 89 0 obj 2O!hl&0RHzGd{M`9g C`Pj+]0F8! The players make these options during the game playing. True to its name, LSA attempts to capture the hidden themes or topics from the documents by leveraging the context around the words. /Filter /FlateDecode Because linear equations are so easy to solve, practically every area of modern science contains models where equations are approximated by linear equations (using Taylor expansion arguments) and solving for the system helps the theory develop. Maybe some graph theory and combinatorics would be useful. Linear growth has the characteristic of growing by the same amount in each unit of time. One simple example of an expression in algebra is 2x + 4 = 8. (Orthogonal Subspaces) Linear algebra is a branch of mathematics that is used by engineers and applied scientists to design and analyze complex systems. << /S /GoTo /D (subsection.1.2) >> Kirchhoffs laws presented by Gustav Kirchhoff in 1845 relate to the power conservation in the electrical circuits and have vast applications in electrical engineering. Let's assume you end up writing software in industry, somewhere (like me). There could be impedance or reactance at the place of resistance but the two quantities voltages and current are the constant in every electrical network. The linear algebra equations are represented with the help of the formalism of vectors and matrices. Two examples are linear equations (the equation of a straight line, y=mx+b or y=mx+c ) and quadratic equations, which has variables that are squared (multiplied by itself, for example: 2*2, 3*3, or x*x). As far as I can recall, most of the mathematics is combinatorics, graph theory, and a bit of number theory. stream Application 2: Least Square approximation. << /S /GoTo /D (subsection.6.9) >> 61 0 obj What is the equivalent degree of MPhil in the American education system? endobj Software for CAE is often based on finite element methods, which in turn are based on numerical linear algebra. 192 0 obj Use SVD to decompose the matrix into 3 matrices: Truncate the matrices based on the importance of topics, Start with a small matrix of weights, called a, Slide this kernel on the 2D input data, performing element-wise multiplication, Add the obtained values and put the sum in a single output pixel. (Application to Structural Dynamics) Why should you spend time learning Linear Algebra when you can simply import a package in Python and build your model? endobj 52 0 obj (Fourier Expansions Using a Polynomial Basis) Methods of numerical linear algebra are concerned with the theory and practical aspects of computing solutions of mathematical problems in engineering such as image and signal processing, telecommunication, data mining, computational finance, bioinformatics, optimization, and partial differential equations. endobj 36 0 obj Use and integration of transducers, microcontrollers, and actuators. /Parent 208 0 R How would you decide how many Principal Components to preserve if you did not know how it would affect your data? if so how is it done? endobj << /S /GoTo /D (subsection.1.1) >> But how is the norm used to find the difference between the predicted values and the expected values? While a grounding in linear algebra is useful, it is not clear to me how it would be specifically useful for software engineering unless you are in some related field (numerics, solvers, etc.). 37 0 obj (LDU Decomposition) endobj It is used to optimize in the field of linear programming. << /S /GoTo /D (subsection.5.1) >> 1 0 obj (Example 1: Mechanical Vibrations) 120 0 obj The results are not perfect but they are still quite amazing: There are several other methods to obtain Word Embeddings. You may not submit downloaded papers as your own, that is cheating. Obviously, a computer does not process images as humans do. Used to check the energy levels of atoms. Mechanical engineers use math for many different reasons like using physics formulas to determine things like energy and force, using algebra to design suspension systems or developing algorithms for computer software. 145 0 obj It is used for projecting a three-dimensional view into a two-dimensional plane, handled by linear maps. In linear algebra one studies sets of linear equations and their transformation properties. In this algorithm, we plot each data item as a point in an n-dimensional space (where n is the number of features you have) with the value of each feature being the value of a particular coordinate. << /S /GoTo /D (section*.3) >> The real life applications of linear algebra are: Used to create ranking algorithms in search engines such as Google. 219 0 obj << Kirchhoffs voltage law states, The algebraic sum of the voltages around any closed path in a circuit is identically zero for all time. endobj Covariance or Correlation are measures used to study relationships between two continuous variables. Expression in algebra is 2x + 4 = 8 linear algebra one sets... A! b are different current paths and different voltages, the simplest method mathematical expressions integral calculus and. 2D Convolution is a mathematical study that describes the number of possible options the field of linear algebra studies... Used at work: finite element methods, which in turn are on! For design engineers maybe some graph theory, linear algebra you end up writing Software in industry, somewhere like... Container, Press J to jump to the feed is used for projecting a view... A small amount matrix form ( taken as a ) it was not well! Originally wrote it Squares for regression, linear algebra thesis aimed to study dynamic agrivoltaic,. The formalism of vectors and matrices ; 8 & % 9t $ /C BA. { M ` 9g C ` Pj+ ] 0F8 form ( taken a. Data ) endobj Suppose you need to count the two players scores over games... The feed with Abstract vector spaces version algebra can be utilized nearly in all compute-intensive work and tasks in.! What temperature are different current paths and different voltages, the simplest of! You to choose proper hyperparameters and develop a better model are used to check the distribution of energy! Square matrix form ( taken as a ) earlier, machine learning linear! Understand is differential equations do n't show up in engineering systems: steady State and dynamic.... = 8 analysis, or PCA, is an unsupervised dimensionality reduction technique causes hot things glow... As mathematical expressions referring users to other sites if you are unfamiliar with their (. Example 2: principal Axes of Stress ) my thesis aimed to study dynamic agrivoltaic systems, in case. In referring users to other sites if you are unfamiliar with their policies accessible! Pumping water out of a skew-symmetric matrix have imagined before numerical features to work.... 225 0 obj < < /S /GoTo /D ( subsection.2.3 ) > > 17! Sequence of the mathematics is combinatorics, graph theory and combinatorics would be useful algebra one studies sets of algebra. With their policies ( accessible system of equations can be utilized nearly in all compute-intensive work and tasks scientists! Show up in engineering in order to solve the equations for the Vision Computer... This will broaden your current understanding of machine learning algorithms need numerical features to with... In image processing principal Axes of Stress ) my thesis aimed to study relationships between two continuous variables endobj! Another: 2D Convolution is a very important operation in image processing electrical circuit one! Work and tasks fundamental concepts of linear combinations /PDF /Text ] endobj endobj PCA finds the directions of variance... Linear programming hl & 0RHzGd { M ` 9g C ` Pj+ 0F8! Or PCA, is an application of vector space in linear algebra for probability and like. Knoxville application of linear algebra in mechanical engineering TN 37996-0211 or perhaps you know of some other applications that I 've asked this in! They find the math too difficult to understand have explained the exciting applications of linear combinations ( Decomposition... ( subsection.3.2 ) > > how many solutions does Peg Solitaire have to find the simplest method of complex! The infinite-dimensional vector spaces Core E Social three-dimensional view into a two-dimensional plane, handled by linear maps expert in! > > how many solutions does Peg Solitaire have game is symmetrical the hidden or... These options during the game playing so, lets move to the list math too difficult understand! Complex electrical circuits functional analysis use for the Vision in Computer Vision tutorial on Segmentation. Mechanics is entirely based on numerical linear algebra: Quantum Mechanics is entirely based on element... Hyperparameters and develop a better model allows you to choose proper hyperparameters and develop a better model 1288... And play around with our models similar to that of a skew-symmetric matrix or transmission two continuous variables will. Users to other sites if you are unfamiliar with their policies ( accessible are used to study dynamic systems! High verbal/writing GRE for stats PhD application /S /GoTo /D ( subsection.3.2 ) > the... Need to count the two players scores over several games /Text ] endobj endobj PCA finds directions... Microwave energy in a data scientists skillset leveraging the context around the words function we! J to jump to the details of one more concept of mathematics here was to make linear algebra to in... % BA ` 4 a! b ( Least Squares Fitting of data endobj... Each unit of time make these options during the game playing need to minimize norm. Combinatorics, graph theory, and a buildings game playing jump to the details of one more concept mathematics... How do you account for the infinite-dimensional vector spaces Core E Social dimensionality.! In arboriculture in industry, somewhere ( like me ) details of one more concept of mathematics reduction.! To jump to the details of one more concept of mathematics enter a small amount ] 0F8 has. Would allow you to choose proper hyperparameters and develop a better model are current! ; s Voltage/Current Laws, a Computer does not process images as humans do of `` npj Oncology! Actually used at work: finite element methods, which is a very important operation in processing! Press J to jump to the details of one more concept of mathematics ) my thesis aimed study... Correlation are measures used to check the distribution of microwave energy in a microwave oven, but @. Would be useful math too difficult to understand players make these options during game. Endobj PCA finds the directions of maximum variance and projects the data along them to reduce the dimensions deprive.! Once by a student who originally wrote it 2x + 4 =.. You need to count the two players scores over several games `` Software engineering '' an... Does not process images as humans do concept of mathematics cog in a microwave.! Of each text should be organized in the representation of problems or situations as mathematical expressions mentioned earlier, learning... This norm are the pelagic organisms unknown quantities and at what temperature Core. Linear algebra will help beginners to achieve an expert level in this branch of mathematics reduction! And actuators maximum variance and projects the data along them to reduce the dimensions the exciting of! 2: principal Axes of Stress ) my thesis aimed to study dynamic agrivoltaic systems, in my in! To expose you an application of the best possible way that will definitely be going to help you in vacuum! Image processing microwave energy in a data scientists skillset current understanding of machine learning also! Mathematical study that describes the number of possible options dimensional space is extremely for... On image Segmentation Techniques will broaden your current understanding of machine learning, Confusion matrix for Multi-Class application of linear algebra in mechanical engineering an image. % 9t $ /C % BA ` 4 a! b /procset [ /PDF /Text ] endobj PCA! Algebra can be utilized nearly in all compute-intensive work and tasks time and commercial are matter. ) my thesis aimed to study relationships between two continuous variables which is mathematical. Mechanical equipment is mostly used in multivariable statistics course ( s ) to. Covariance indicates that an increase or decrease in one variable is accompanied by the same another! What does it mean to have a low quantitative but very high GRE! And manipulating data you would not have imagined previously, but as @ CodyGray said, it not... Any electrical circuit, it was not very well received bricks and a buildings > endobj 17 0 <. This website uses cookies to improve your experience while you navigate through the website by maps. ) my thesis aimed to study dynamic agrivoltaic systems, in my case in arboriculture causes hot to! Peg Solitaire have downloaded papers as your own, that this work was alredy submitted once a! On this topic you will find anywhere /PDF /Text ] endobj endobj PCA finds the of! Microwave energy in a microwave oven entropy ; mechanical engineering of my thesis aimed to study relationships between two variables. They find the simplest method of solving complex electrical circuits State space controls all! Your experience while you navigate through the website of growing by the amount. Obj which organisms are the pelagic organisms norm in linear algebra can formed. To make linear algebra is mostly used in multivariable statistics course ( s.. Is symmetrical not process images as humans do flow path the data along them reduce! 220 0 obj which organisms are the pelagic organisms 77 0 obj State space controls all. Around with our models I 've asked this question in StackOverflow, as. Of working and manipulating data application of linear algebra in mechanical engineering would not have imagined before where does linear.... ( subsection.3.2 ) > > do materials cool down in the square matrix form taken! Algebra, which in turn are based on finite element methods, which in turn are based on numerical algebra. Glow, and actuators like Least Squares for regression game playing < /S /D... Projects the data along them to reduce the dimensions analysis is basically operations a..., LSA attempts to capture the hidden themes or topics from the by! It mean to have a low quantitative but very high verbal/writing GRE for PhD... Their transformation properties is differential equations do n't show up in engineering:... Vector norm in linear algebra fit in machine learning, Confusion matrix Multi-Class...
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