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:
“Navarette, a Chinese missionary, agrees with Leibniz and says that “It is the special providence of God that the Chinese did not know what was done in Christendom; for if they did, there would be never a man among them, but would spit in our faces.””
—Matthew Tindal (1653–1733)
“Lovers’ quarrels are not generally about money. Divorce cases generally are.”
—Mason Cooley (b. 1927)