Transpose of a matrix
This functionality does not run in MATLAB.
transpose(A
)
transpose(A)
returns the transpose A^{t} of
the matrix A.
The transpose of the m×n matrix A is the n×m matrix B with B_{i, j} = A_{j, i}.
If the input is a matrix of category Cat::Matrix
, then linalg::transpose
is called to compute
the result. In contrast to the linalg routines, the function transpose
also
operates on array
s
and hfarray
s.
If the argument does not evaluate to a matrix of one of the
types mentioned above, symbolic call transpose(A)
is
returned.
The following matrix is real. Thus, the Hermitian transpose coincides with the transpose:
A := array(1..2, 1..2, [[1, 2], [3, PI]])
transpose(A) = htranspose(A)
In general, this does not hold for complex matrices:
A := hfarray(1..2, 1..3, [[1, I, 3 + I], [PI*I, 4, 5]])
transpose(A) <> htranspose(A)
delete A:
We 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 symbolic calls are returned:
delete A, B: transpose(A) + 2*htranspose(B)

A matrix: either a 2dimensional 
Matrix of the same domain type as A
.
A