Conjugate transpose - Wikipedia

Abstraction: Conjugate transpose operation, notations, and matrix classification by self-adjointness

Key points:

• Conjugate transpose of complex matrix A is formed by transposing then taking complex conjugate of each entry; notations A^*, A^H, A^† used across disciplines
• For real matrices, conjugate transpose reduces to ordinary transpose
• A square matrix is Hermitian if A = A^H; skew-Hermitian if A = -A^H; normal if A^H A = A A^H; unitary if A^H A = I
• Key property: (AB)^H = B^H A^H (product order reverses)
• Eigenvalues of A^H are complex conjugates of eigenvalues of A
• Arises naturally when representing complex numbers as 2x2 real rotation matrices — transposing such a representation corresponds to complex conjugation

Connections: Conjugate Transpose · Hermitian Matrix · Linear Algebra · Wikipedia

Source: http://en.wikipedia.org/wiki/Conjugate_transpose