In linear algebra, a square matrix A is diagonalizable if it is similar to a diagonal matrix, that is, if there exists an invertible matrix P such that P−1AP is a diagonal matrix.
Diagonalizable matrices and maps are of interest because diagonal matrices are especially easy to handle. If their eigenvalues and eigenvectors are known, one can raise a diagonal matrix to a power by simply raising the diagonal entries to that same power, and the determinant of a diagonal matrix is simply the product of all diagonal entries.