Algorithm for an elimination matrix

Question

Luciano Campos 2016-3-18

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https://ww2.mathworks.cn/matlabcentral/answers/274256-algorithm-for-an-elimination-matrix

评论： Luciano Campos 2016-3-18

Hi everybody, Can anybody help me to design a Matlab code function that creates an elimination matrix L of size (.5m(m+1),m^2) such that, for a (m,m) square matrix A:

vech(A)=L vec(A)

where the vech and vec operators are such that, for example, if:

Thanks for your help,

best,

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Answer 1

James Tursa 2016-3-18

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https://ww2.mathworks.cn/matlabcentral/answers/274256-algorithm-for-an-elimination-matrix#answer_214142

编辑：James Tursa 2016-3-18

在 MATLAB Online 中打开

m = size(A,1); % Size of A
T = tril(ones(m)); % Lower triangle of 1's
f = find(T(:)); % Get linear indexes of 1's
k = m*(m+1)/2; % Row size of L
m2 = m*m; % Colunm size of L
L = zeros(m2,k); % Start with L'
x = f + m2*(0:k-1)'; % Linear indexes of the 1's within L'
L(x) = 1; % Put the 1's in place
L = L'; % Now transpose to actual L