Definition
diagonalizable
adjective
- (of a matrix) capable of being transformed into a diagonal matrix through a change of basis; having a complete set of linearly independent eigenvectors.
Usage: technical; mathematics
Examples
- A symmetric matrix is always diagonalizable over the real numbers.
- The professor asked us to determine whether the given matrix is diagonalizable.
- Not every square matrix is diagonalizable; some lack enough independent eigenvectors.
- If a matrix is diagonalizable, we can simplify many calculations by working with its diagonal form.
- The eigenvalues and eigenvectors help us understand whether a matrix is diagonalizable.