Diagonalizable
Diagonalizable refers to a square matrix or linear operator that can be represented as a diagonal matrix in some basis. A matrix A over a field F is diagonalizable over F if there exists an invertible P in F^{n×n} such that P^{-1}AP is diagonal. Equivalently, A is diagonalizable if there exists a basis consisting entirely of eigenvectors of A; in that case A can be written as A = PDP^{-1}, where D is diagonal and contains the eigenvalues of A on its diagonal.
Several equivalent criteria are commonly used. If A has n distinct eigenvalues in F, then A is
Examples illustrate the concept. The identity matrix is diagonalizable. Any diagonal matrix is diagonalizable. If a