Diagonalization theorem: a nxn matrix A is diagonalizable if and only if it has n linearly independent eigenvectors. If so, the matrix factors as A = PDP^{-1}, where D is diagonal and P is invertible (and its columns are the n linearly independent eigenvectors). Algorithm to diagonalize a matrix.

- Created On
- August 25th, 2017
- 6 years ago
- Views
- 3
- Type
- Video
- Language
- English
- Content Type
- text/html; charset=utf-8

##### Definition of diagonalizable matrix math.la.d.mat.diagonalizable

##### An n-by-n matrix is diagonalizable if and only if it has n linearly independent eigenvectors. math.la.t.mat.diagonalizable

##### A diagonalizable matrix is diagonalized by a matrix having the eigenvectors as columns. math.la.t.mat.diagonalized_by

##### An n-by-n matrix with n distinct eigenvalues is diagonalizable. math.la.t.mat.diagonalizable.distinct