Home > freetb4matlab > linear-algebra > commutation_matrix.m

commutation_matrix

PURPOSE ^

% Return the commutation matrix

SYNOPSIS ^

function k = commutation_matrix (m, n)

DESCRIPTION ^

% -*- texinfo -*-
% @deftypefn {Function File} {} commutation_matrix (@var{m}, @var{n})
% Return the commutation matrix
% @iftex
% @tex
%  $K_{m,n}$
% @end tex
% @end iftex
% @ifnottex
%  K(m,n)
% @end ifnottex
%  which is the unique
% @iftex
% @tex
%  $m n \times m n$
% @end tex
% @end iftex
% @ifnottex
%  @var{m}*@var{n} by @var{m}*@var{n}
% @end ifnottex
%  matrix such that
% @iftex
% @tex
%  $K_{m,n} \cdot {\rm vec} (A) = {\rm vec} (A^T)$
% @end tex
% @end iftex
% @ifnottex
%  @math{K(m,n) * vec(A) = vec(A')}
% @end ifnottex
%  for all
% @iftex
% @tex
%  $m\times n$
% @end tex
% @end iftex
% @ifnottex
%  @math{m} by @math{n}
% @end ifnottex
%  matrices
% @iftex
% @tex
%  $A$.
% @end tex
% @end iftex
% @ifnottex
%  @math{A}.
% @end ifnottex
%
% If only one argument @var{m} is given,
% @iftex
% @tex
%  $K_{m,m}$
% @end tex
% @end iftex
% @ifnottex
%  @math{K(m,m)}
% @end ifnottex
%  is returned.
%
% See Magnus and Neudecker (1988), Matrix differential calculus with
% applications in statistics and econometrics.
% @end deftypefn

CROSS-REFERENCE INFORMATION ^

This function calls: This function is called by:
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