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Problem computing determinant
Posted:
Aug 16, 1996 5:35 PM
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I am having a problem computing the determinant of a matrix.
Specifically, I am solving an eigenvalue problem, and then using
the original matrix and one of the eigenvalues and checking
that the determinant is zero.
n=5;
A=random('T',1,n,n);
[x,l]=eig(R);
det(A-eye(size(A))*l(1,1))
From det(A-lI)=0, the eigenvalues, l, can be found. So The result
of the last line of the script should be close to zero. This works
acceptable for small matricies (n<8). When n>10, the value of the
determinant is on the order of 0.1-1. Here the result is dependent
on the numbers generated by the random statement.
For n=100, I check the orthogonality of the eigenvectors, and the
results from the diagonalization of the system.
For orthogonality and diagonalization, the results are accurate to at
least 10e-6. However the determinant of A-lI for any of the eigenvalues
found is ~10e260!
Am I trying to do something real stupid, or is it really roundoff error.
Does the determinant function return the product of the diagonal elements
of U from an LU decomposition?
It is hard to believe that the eigenvectors are that accurate, but the
determinant cannot be found as accurate.
Thanks,
Craig
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