This video *derives* the eigenvalues and eigenvectors of a matrix "A" to solve the matrix system of equations dx/dt = A*x.
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
1:26 Problem Setup
2:33 The Simplest System of ODEs: Decoupled (Diagonal) Dynamics
10:25 Finding a Coordinate System Where Dynamics Look Diagonal
15:42 Deriving the Eigenvalue/Eigenvector Equation
19:03 A Picture of the Eigenvalue Equation
22:27 Recap and Summary