Conjugate transpose

In mathematics, the conjugate transpose, also known as the Hermitian transpose, of an m × n {\displaystyle m\times n} complex matrix A {\displaystyle \mathbf {A} } is an n × m {\displaystyle n\times m} matrix obtained by transposing A {\displaystyle \mathbf {A} } and applying complex conjugation to each entry (the complex conjugate of a + i b {\displaystyle a+ib} being a − i b {\displaystyle a-ib} , for real numbers a {\displaystyle a} and b {\displaystyle b} ). There are several notations, such as A H {\displaystyle \mathbf {A} ^{\mathrm {H} }} or A ∗ {\displaystyle \mathbf {A} ^{*}} ,[1] A ′ {\displaystyle \mathbf {A} '} ,[2] or (often in physics) A † {\displaystyle \mathbf {A} ^{\dagger }} .