Basic Remarks
A square matrix A with entries is called
- Hermitian or self-adjoint if A = A*, i.e., .
- skew Hermitian or antihermitian if A = −A*, i.e., .
- normal if A*A = AA*.
- unitary if A* = A-1.
Even if A is not square, the two matrices A*A and AA* are both Hermitian and in fact positive semi-definite matrices.
The conjugate transpose "adjoint" matrix A* should not be confused with the adjugate adj(A), which is also sometimes called "adjoint".
Finding the conjugate transpose of a matrix A with real entries reduces to finding the transpose of A, as the conjugate of a real number is the number itself.
Read more about this topic: Conjugate Transpose
Famous quotes containing the words basic and/or remarks:
“The research on gender and morality shows that women and men looked at the world through very different moral frameworks. Men tend to think in terms of “justice” or absolute “right and wrong,” while women define morality through the filter of how relationships will be affected. Given these basic differences, why would men and women suddenly agree about disciplining children?”
—Ron Taffel (20th century)
“I begin, then, with some remarks about ‘the meaning of a word.’ I think many persons now see all or part of what I shall say: but not all do, and there is a tendency to forget, or to get it slightly wrong. In so far as I am merely flogging the converted, I apologize to them.”
—J.L. (John Langshaw)