~^ (Matrix Conjugate Transpose)

Purpose:

Complex conjugate transpose of a matrix.

A~^

An array or series.

An NxM array where the input is an MxN array.

W1: {{i, 2, 3},

{1, 2i, 3},

{1, 2, 3i}}

W2: W1~^

W2 == {{0 – 1i, 1 + 0i, 1 + 0i},

{2 + 0i, 0 – 2i, 2 + 0i},

{3 + 0i, 3 + 0i, 0 – 3i}}

W3 : W1’

W3 == {{0 + 1i, 1 + 0i, 1 + 0i},

{2 + 0i, 0 + 2i, 2 + 0i},

{3 + 0i, 3 + 0i, 0 + 3i}}

The postfix A~^ operator is equivalent to transposeconj(A) and is equivalent to conj(transpose(A)) . For example:

b = conj(transpose(A))

b = transposeconj(A)

b = A~^

are equivalent.

For a real array, ~^ and ‘ are equivalent.