Let the operator vec($A$) unroll all the elements of $A$ into a single column vector in column-major order. Then, the elements of vec($A^T$) are a permutation of the elements of vec($A$). If I want to write this permutation as a matrix-vector product, I get


vec($A^T)$ = $P$ vec($A$).


I'm looking for a common name and/or symbol for the "vec transposition permutation matrix" $P$?



Better name for “vec transposition permutation matrix”?
This matrix is known as the *commutation matrix*. For more details, please see Chapter 3, Section 7 of: [Matrix differential calculus](http://www.janmagnus.nl/misc/mdc2007-3rdedition) by Magnus and Neudecker.


