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Title | Dhruv On Math |
Description | Interactive Visualization of Why Eigenvectors Dhruv On Math About All Posts Feed Interactive Visualization of Why Eigenvectors Matter 26 Jul 2020 You’ve probably heard the word eigenvectors hundreds o |
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WebSite | dhruvonmath.com |
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US$2,353,280
Last updated: 2022-07-13 23:00:05
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Dhruv On Math About All Posts Feed Interactive Visualization of Why Eigenvectors Matter 26 Jul 2020 You’ve probably heard the word eigenvectors hundreds of times in class and have been asked to calculate it hundreds more. But why is this concept so central in Linear Algebra? Why is it that we study the eigenvector of a matrix so often? In this post, we’ll see how Eigenvectors help us immediately understand what a linear function will do to an input. We’ll do so by playing with an interactive visualization that allows us to see just that. Quick Refresher Here, applying A A A on its eigenvector v v v leades to a new vector λ v \lambda v λ v is in the same direction as v v v . Image Source: Wikipedia. Let’s do a quick refresher to begin with. The eigenvector of a linear function A A A is just the vector v v v s.t. A v = λ v Av = \lambda v A v = λ v for some constant λ \lambda λ which we call the eigenvalue. At a high level, the eigenvector is just a dimension along which the linear |
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