Conjugate Transpose -- from Wolfram MathWorld

Abstraction: Definition and notation of the matrix conjugate transpose operation

Key points:

• Conjugate transpose of matrix A is formed by transposing then complex-conjugating all entries; also called adjoint, adjugate, Hermitian adjoint, or Hermitian transpose
• Notations include A^H (common in linear algebra), A^* (quantum field theory), A^† (physics dagger notation)
• In separable Hilbert spaces, conjugate and transpose operations commute
• A matrix equal to its own conjugate transpose is self-adjoint (Hermitian)
• Product rule: (AB)^H = B^H A^H (order reverses)
• Implemented in Wolfram Language as ConjugateTranspose[A]

Connections: Conjugate Transpose · Hermitian Matrix · Linear Algebra · Wolfram Mathworld

Source: http://mathworld.wolfram.com/ConjugateTranspose.html