Note that the eigenvalues appear in the diagonal matrix.

A diagonal matrix is one whose off-diagonal entries are all zero.

In this type of transformation the 3x3 matrix is a diagonal matrix.

The product of two anti-diagonal matrices is a diagonal matrix.

Complex numbers are block diagonal matrices with two 2x2 blocks.

Where is a diagonal matrix sorted in increasing order.

In the general case, let T be the subgroup of diagonal matrices.

We now establish an important property of diagonal matrices.

For example, if then where is the diagonal matrix of the squares of the eigenvalues.

In this case, we cannot reduce C to a diagonal matrix of units, since evidently.