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transpose

Transpose of a matrix

Use only in the MuPAD Notebook Interface.

This functionality does not run in MATLAB.

Syntax

transpose(A)

Description

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.

Examples

Example 1

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:

Example 2

We compute the product AHA 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 AHA is Hermitian:

AH*A = htranspose(AH*A)

delete A, AH:

Example 3

If the input does not evaluate to a matrix, then symbolic calls are returned:

delete A, B:
transpose(A) + 2*htranspose(B)

Parameters

A

A matrix: either a 2-dimensional array, a 2-dimensional hfarray, or an object of the category Cat::Matrix

Return Values

Matrix of the same domain type as A.

Overloaded By

A

See Also

MuPAD Functions

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