This video explores the eigenvalues and eigenvectors of a matrix "A". This is one of the most important concepts in linear algebra. The eigenvectors represent a change of coordinates in which the "A" matrix becomes diagonal, with entries given by the eigenvalues. This allows us to easily solve arbitrarily complex linear systems of differential equations.
Playlist: https://www.youtube.com/playlist?list=PLMrJAkhIeNNTYaOnVI3QpH7jgULnAmvPA
Course Website: http://faculty.washington.edu/sbrunton/me564/
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This video was produced at the University of Washington
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0:00 Overview and Eigenvalue Equation
3:15 Eigenvalues and Eigenvectors are "Special"
6:00 Example 2x2 Matrix
14:55 Computing Eigenvalues and Eigenvectors for *any* Matrix
21:18 The Determinant Measures Area of a Transformation
25:50 Determinant of 3x3 Matrix
28:35 Revisit 2x2 Matrix Example