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This lecture explains eigenvalues and eigenvectors, including their role in diagonalizing matrices and simplifying linear systems of differential equations. It derives the characteristic equation and works through 2×2 examples and the general computation procedure.
Syllabus
Overview and Eigenvalue Equation
Eigenvalues and Eigenvectors are "Special"
Example 2x2 Matrix
Computing Eigenvalues and Eigenvectors for *any* Matrix
The Determinant Measures Area of a Transformation
Determinant of 3x3 Matrix
Revisit 2x2 Matrix Example
Taught by
Steve Brunton