Matrix diagonalization
Put content here.
Now you are in the subtree of Container for Linear Algebra project.
- Definition of matrix diagonalization
- Definition of diagonalizable matrix
- An n-by-n matrix is diagonalizable if and only if it has n linearly independent eigenvectors.
- An n-by-n matrix is diagonalizable if and only if the sum of the dimensions of the eigenspaces equals n.
- An n-by-n matrix is diagonalizable if and only if the characteristic polynomial factors completely
- A diagonalizable matrix is diagonalized by a matrix having the eigenvectors as columns.
- An n-by-n matrix is diagonalizable if and only if the union of the basis vectors for the eigenspaces is a basis for R^n (or C^n).
- An n-by-n matrix with n distinct eigenvalues is diagonalizable.
- Formula for diagonalizing a real 2-by-2 matrix with a complex eigenvalue.
© KTree Inc. 2024