Given LUP decomposition of a matrix, how to find determinant in MATLAB?

Question

I want to compute the determinant of a matrix from its LUP decomposition in MATLAB. The determinant can be found from the formula:

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P is a permutation matrix and S is the number of exchanges of rows needed to transform P into an identity matrix. How can I find S in the above formula in MATLAB? Does it have any pre-defined functions, etc.?

Jonas · Accepted Answer · 2014-01-10T16:14:41.247

3

If you interpret P as an adjacency matrix, and the vector cycles contains the length of all cycles in the graph described by P, then S=sum(cycles) - length(cycles).

Now all is left is to find the length of all the cycles, for which there are several functions on the File Exchange, like this one.

BTW: [L, U, P] = lu(A), and det(A) = det(inv(P))*det(L)*det(U)

edited Jan 10 '14 at 16:14

answered Jan 10 '14 at 14:20

Jonas

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The function on file exchange does not accept P as an adjacency matrix, because it's not symmetric. What can I do? – user215721 Jan 10 '14 at 16:22
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@user215721 `symmetricP = (P+P)'` – Jonas Jan 10 '14 at 16:31
Thank you very much! (a typo in your above comment: symmetricP=P+P') – user215721 Jan 10 '14 at 17:41

Given LUP decomposition of a matrix, how to find determinant in MATLAB?

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