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:
“Insecurity, commonly regarded as a weakness in normal people, is the basic tool of the actor’s trade.”
—Miranda Richardson (b. 1958)
“So, too, if, to our surprise, we should meet one of these morons whose remarks are so conspicuous a part of the folklore of the world of the radio—remarks made without using either the tongue or the brain, spouted much like the spoutings of small whales—we should recognize him as below the level of nature but not as below the level of the imagination.”
—Wallace Stevens (1879–1955)