conjugate transpose

Definition

The conjugate transpose (i.e. Hermitian transpose, adjoint matrix) $M^*$ of a matrix $M$ is the transpose of the matrix $M$ where each entry is replaced by its complex conjugate, i.e. complex number $a + ib$ becomes $a - ib$ and vice versa.

(note for real matrix, the conjugate transpose simply yields the transpose matrix)

A Hermitian matrix (or self-adjoint matrix) is one satisfying $M = M^*$ (generalization of symmetric matrix for real matrices).

References

1. https://en.wikipedia.org/wiki/Conjugate_transpose
2. https://en.wikipedia.org/wiki/Hermitian_matrix