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Topic: Problem computing determinant
Replies: 1   Last Post: Aug 18, 1996 10:40 PM

 Messages: [ Previous | Next ]
 Craig C. Tierney Posts: 1 Registered: 12/11/04
Problem computing determinant
Posted: Aug 16, 1996 5:35 PM

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

Date Subject Author
8/16/96 Craig C. Tierney
8/18/96 Cleve Moler