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

Department of Mathematics