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## Vectorized Transpose Matrix

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

Updated 24 Feb 2010

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
##### Platform Compatibility
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