A square matrix is said to be diagonalizable if it is similar to a diagonal matrix. That is, A is diagonalizable if there is an invertible matrix P and a diagonal matrix D such that. A=PDP^{-1}. A=PDP−1.

How do you know if a matrix is diagonalizable?

A matrix is diagonalizable if and only if for each eigenvalue the dimension of the eigenspace is equal to the multiplicity of the eigenvalue. Meaning, if you find matrices with distinct eigenvalues (multiplicity = 1) you should quickly identify those as diagonizable.

Are 2x2 matrices always diagonalizable?

Since the 2×2 matrix A has two distinct eigenvalues, it is diagonalizable. To find the invertible matrix S, we need eigenvectors.