Hi, i know 33x33 nnormalized matrix.... i shd multiply with 33 unknowns...matrix multiplication....with same 33 unknowns even on left will be there...... how to calculate these 33 unknowns,..
[x1 x2 x3 ....... x33][Normalized matrix 33x33] = [x1 x2 x3 ..... x33]
help me ,,,
There will be no non-zero solution unless one or more of the eigenvalues of the 33 by 33 matrix is equal to 1. Furthermore there will be no solution with a sum of 1 unless there is a corresponding eigenvector with a non-zero sum. Therefore, use matlab's 'eig' function to find its eigenvalues and eigenvectors and if one of the eigenvalues is 1 with a corresponding eigenvector whose sum is non-zero, normalize that eigenvector (divide its elements by their sum) to have sum 1 and that will be a solution.
I didn't realize that by "33x33 nnormalized matrix" you meant that its rows each have a sum of 1. In that case I believe there will be at least one eigenvalue of 1 and my warning no longer applies. You can solve for your vector as follows. Let A be your 33 x 33 matrix in which each row has a sum of 1.
[V,D] = eig(A'); % Find eigenvalues and left eigenvectors of A [~,ix] = min(abs(diag(D)-1)); % Locate an eigenvalue which equals 1 v = V(:,ix)'; % The corresponding row of V' will be a solution v = v/sum(v); % Adjust it to have a sum of 1
The vector v will be the vector you seek.