In mathematics, the conjugate transpose (or Hermitian transpose) of an m-by-n matrix A {\displaystyle {\boldsymbol {A}}} with complex entries is the n-by-m matrix obtained from A {\displaystyle {\boldsymbol {A}}} by taking the transpose and then taking the complex conjugate of 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} ). It is often denoted as A H {\displaystyle {\boldsymbol {A}}^{\mathrm {H} }} or A ∗ {\displaystyle {\boldsymbol {A}}^{*}} .
For real matrices, the conjugate transpose is just the transpose, A H = A T reference
