conjugate transpose

conjugate transpose (plural conjugate transposes)

1. (mathematics) The transpose of a matrix, after replacing each element with its complex conjugate.

In linear algebra, it may be denoted using the notations A^*, A^H, A^† or A⁺. Of these, the superscripted dagger (glyph) notation is universally used in quantum mechanics. Also, the notation A⁺ is commonly used for the Moore–Penrose pseudoinverse.

In some contexts, A^* denotes the matrix of complex conjugate entries, and the transpose conjugate is then denoted by A^*T or A^T*.

• (transpose of matrix of complex conjugates): adjoint matrix, bedaggered matrix, conjugate transpose, Hermitian conjugate, Hermitian transpose, transjugate

• adjugate matrix (historically also sometimes called "adjoint")

• transpose conjugate