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
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