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:
“He’s leaving Germany by special request of the Nazi government. First he sends a dispatch about Danzig and how 10,000 German tourists are pouring into the city every day with butterfly nets in their hands and submachine guns in their knapsacks. They warn him right then. What does he do next? Goes to a reception at von Ribbentropf’s and keeps yelling for gefilte fish!”
—Billy Wilder (b. 1906)
“You all know that even when women have full rights, they still remain fatally downtrodden because all housework is left to them. In most cases housework is the most unproductive, the most barbarous and the most arduous work a woman can do. It is exceptionally petty and does not include anything that would in any way promote the development of the woman.”
—Vladimir Ilyich Lenin (1870–1924)