Unexpected result calculating the determinant of a singular matrix (42S)

[Valentin Albillo]

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Hi, Dave:

(10-21-2019 01:54 AM)Dave Britten Wrote:  When calculating the determinant of the matrix [[-2,1,3][1,2,1][3,1,-2]] on my 42S, I would expect to get 0 as it is a singular matrix. But the 42S says it's 3.30000000001E-12. How does the 42S calculate determinants that would lead to that result? And how do I identify when it's giving me a suspicious result? I've done very little linear algebra, so there might be something simple and obvious going on here.

The 42S uses LU-decomposition to compute determinants. This process involves divisions so inexact terms are produced and thus rounding errors do creep in and that's why you don't get an exact result sometimes, even if the matrix has all integer elements and it's as small as 2x2.

For an exact way to compute determinants download and have a look at my PDF paper:

Exact Determinants and Permanents

which includes a program and revealing examples.

Regards.
V.