Hermitian transpose of a matrix
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htranspose(A) returns the Hermitian transpose AH 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 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)
Compute the product AH 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]])
The product AH 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)
Object of the same domain type as