A **diagonal matrix** is a square matrix whose only non zero entries are on the diagonal, i.e.
*A*=(*a*_{ij}) is
diagonal if, and only if,
.
If the diagonal entries are
,
we denote
.

For example, is a diagonal matrix.

A square matrix *A* is **diagonalizable** if there exists an invertible matrix *P* such that *P*^{-1}*AP* is a
diagonal matrix.

The matrix *P* is the change of base matrix from the standard basis to the basis of eigenvectors.