The conjugate transpose, also known as Hermitian transpose, performs complex conjugate on each element of a complex matrix and then transpose it. There are several notations, such as , , , and (often in physics) . 1

For example, the conjugate transpose of a 2x2 matrix is Where , , , represent the complex conjugates of each elements.

For a real matrix, the conjugate transpose is just the transpose: . 1

  • A complex square matrix is unitary is

Footnotes

  1. Conjugate transpose - Wikipedia 2