Hermitian transpose of a matrix
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htranspose(A
)
htranspose(A)
returns the Hermitian transpose A^{H} of
the matrix A (the
complex conjugate of the transpose of A).
The Hermitian transpose of the m×n matrix A is
the n×m matrix B with
.
If the input is a matrix of category Cat::Matrix
, then internally linalg::htranspose
computes
the result. For arrays
and hfarrays
, htranspose
uses
other routines.
If the argument does not evaluate to a matrix of one of these types, the transpose is the conjugate of the input.
Compute the transpose of the following real matrix. For real matrices, the Hermitian transpose coincides with the transpose:
A := matrix([[1, 2], [3, PI]])
transpose(A) = htranspose(A)
In general, this does not hold for complex matrices:
A := matrix([[1, I, 3 + I], [PI*I, 4, 5]])
transpose(A) <> htranspose(A)
delete A:
Compute the product A^{H} A of
a matrix given by a hardware float array
. This data type
allows matrix multiplication using the operator *
:
A := hfarray(1..2, 1..3, [[1, I, 3], [PI*I, 4, 5 + I]])
AH:= htranspose(A)
The product A^{H} A is Hermitian:
AH*A = htranspose(AH*A)
delete A, AH:
If the input does not evaluate to a matrix, then the transpose is the conjugate of the input:
htranspose(A) + 2*htranspose(B)

An object of the category 
Object of the same domain type as A
.
A