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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(Aeye(size(A))*l(1,1))
From det(AlI)=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 0.11. 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 10e6. However the determinant of AlI 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



