Special Cases
Among complex matrices, all unitary, Hermitian, and skew-Hermitian matrices are normal. Likewise, among real matrices, all orthogonal, symmetric, and skew-symmetric matrices are normal.
However, it is not the case that all normal matrices are either unitary or (skew-)Hermitian. As an example, the matrix
is normal because
The matrix A is neither unitary, Hermitian, nor skew-Hermitian.
The sum or product of two normal matrices is not necessarily normal. If they commute, however, then this is true.
If A is both a triangular matrix and a normal matrix, then A is diagonal. This can be seen by looking at the diagonal entries of A*A and AA*, where A is a normal, triangular matrix.
Read more about this topic: Normal Matrix
Famous quotes containing the words special and/or cases:
“A successful woman preacher was once asked “what special obstacles have you met as a woman in the ministry?” “Not one,” she answered, “except the lack of a minister’s wife.””
—Anna Garlin Spencer (1851–1931)
“And in cases where profound conviction has been wrought, the eloquent man is he who is no beautiful speaker, but who is inwardly drunk with a certain belief. It agitates and tears him, and perhaps almost bereaves him of the power of articulation.”
—Ralph Waldo Emerson (1803–1882)