In
mathematics, the
conjugate transpose or
Hermitian transpose of an
m-by-
n matrix with
complex entries is the
n-by-
m matrix
* obtained from by taking the
transpose and then taking the
complex conjugate of each entry (i.e., negating their imaginary parts but not their real parts). The conjugate transpose is formally defined by
where the subscripts denote the
i,
j-th entry, for 1 =
i =
n and 1 =
j =
m, and the overbar denotes a scalar
complex conjugate. (The complex conjugate of
, where
a and
b are reals, is
.)