Transpose of a matrix
This functionality does not run in MATLAB.
transpose(A) returns the transpose At of the matrix A.
The transpose of the m ⨉ n matrix A is the n ⨉ m matrix B with Bi, j = Aj, 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 arrays and hfarrays.
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)
We 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 symbolic calls are returned:
delete A, B: transpose(A) + 2*htranspose(B)