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Vectorized Transpose Matrix

version 1.0.0.0 (1.35 KB) by Zachary Danziger
Creates an orthogonal permutation matrix for tensor and linear algebra manipulations.

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Updated 24 Feb 2010

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The vectorized transpose matrix, Tmn, is the matrix that permutes the vectorization of an m#n matrix A into its transpose vectorization. For example, if the vectorization of A is defined as vec(A), or A(:), then Tmn*vec(A) = vec(A').

EXAMPLE
The vectorized transpose matrix can be used to reverse the order of arguments to the otherwise non-commutative Kronecker product.

>> m=2;n=3;p=4;q=2;
>> A = rand(m,n); B = rand(p,q);
>> isequal(TvecMat(p,m)*kron(A,B)*TvecMat(n,q),kron(B,A))
ans =
1

For other useful properties of the vectorized transpose matrix, see:
http://www.ee.ic.ac.uk/hp/staff/dmb/matrix/special.html#VecTranspose

Cite As

Zachary Danziger (2021). Vectorized Transpose Matrix (https://www.mathworks.com/matlabcentral/fileexchange/26781-vectorized-transpose-matrix), MATLAB Central File Exchange. Retrieved .

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MATLAB Release Compatibility
Created with R2009a
Compatible with any release
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