Hermitian conjugate matrix

In mathematics, the conjugate transpose, also known as the Hermitian transpose, of an complex matrix is an matrix obtained by transposing and applying complex conjugate on each entry (the complex conjugate of being , for real numbers and ). It is often denoted as or or or (often in physics) . For real matrices, the conjugate transpose is just the transpose, . Definition The conjugate transpose of an matrix is formally defined by where the subscript denotes the -th entry, for and , and the overbar denotes a scalar complex conjugate.