Definition:Diagonalizable Matrix
Jump to navigation
Jump to search
Definition
A diagonalizable matrix $\mathbf A$ is a square matrix which is similar to a diagonal matrix.
That is, $\mathbf A$ is diagonalizable if and only if there exists an invertible matrix $\mathbf X$ such that $\mathbf X^-1 \mathbf A \mathbf X$ is a diagonal matrix.
Also see
- Results about diagonalizable matrices can be found here.
Sources
- 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): diagonalizable matrix
- 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): diagonalizable matrix