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The Matrix Computation Toolbox

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The Matrix Computation Toolbox

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11 Sep 2002 (Updated )

A collection of M-files for carrying out various numerical linear algebra tasks.

vecperm(m, n)
function P = vecperm(m, n)
%VECPERM    Vec-permutation matrix.
%           VECPERM(M, N) is the vec-permutation matrix, an MN-by-MN
%           permutation matrix P with the property that if A is M-by-N then
%           vec(A) = P*vec(A').
%           If N is omitted, it defaults to M.

%   P is formed by taking every n'th row from EYE(M*N), starting with
%   the first and working down - see p. 277 of the reference.

%   Reference:
%   H. V. Henderson and S. R. Searle The vec-permutation matrix,
%   the vec operator and Kronecker products: A review Linear and
%   Multilinear Algebra, 9 (1981), pp. 271-288.

if nargin == 1, n = m; end

P = zeros(m*n);
I = eye(m*n);

k = 1;
for i=1:n
    for j=i:n:m*n
        P(k,:) = I(j,:);
        k = k+1;
    end
end

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