## Diagonalizability

To find whether is diagonalizable, we can use the command [P,D] = eig(A) and the function det(P). If det(P) returns 0, or the magnitude of  (for example, 1.2608e-08), is not invertible, and therefore, is not diagonalizable. Otherwise, is invertible, and is diagonalizable.

EXAMPLE 1. Diagonalize each of the following matrices if possible.

Power of diagonalizable matrices

Let be a diagonal matrix with diagonal entities  . Then the -th power  is simply given by

In particular when is diagonalizable, we can express .

Department of Mathematics