Built-in Mathematica Symbol

ConjugateTranspose

gives the conjugate transpose of

.

ConjugateTranspose[m] can also be given as , where can be entered as Esc hc Esc or \[HermitianConjugate].

Conjugate transpose of a complex-valued matrix:

Enter using Esc ct Esc:

Conjugate transpose of a complex-valued matrix:

Out[2]//MatrixForm=

Out[3]//MatrixForm=

Enter using Esc ct Esc:

Conjugate transpose a sparse array:

The conjugate transpose is sparse:

ConjugateTranspose works for symbolic matrices:

ComplexExpand assumes all variables are real:

ConjugateTranspose works similarly to Transpose for tensors:

Conjugate and transpose the first two dimensions:

Conjugate and transpose the first and third dimensions:

is a random complex matrix:

:

is unitary, so its inverse is

Reconstruct

from the decomposition:

The product of a matrix and its conjugate transpose is Hermitian:

is the matrix product of

and

.

so

is Hermitian: