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I want to solve a system of 8 linear integer equations, A y = b.

It's clear that if I knew the exact value of the coefficients I should use one of the methods described here: Solve system of linear integer equations in Python but in my case I have a matrix like

Corrected matrix

and the value of x is known only approximately (and det(A) is approximately 0, but not exactly 0). Is there any way to find a solution of the system in such a case?

gboffi
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user3419643
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    Welcome here User :) But I think this question is a mathematical one and has its place here: https://math.stackexchange.com/ – AlEmerich Oct 26 '18 at 08:04
  • So you have an eigenvalue problem in which you cannot find the correct eigenvalues (because of numerical issues) but you want an approximation of the eigenvectors... am I right or am I wrong? In the first case, I'd rewrite the question (or delete the question and write a new one), considering also the possibility of posting on math stackexchange. That said, when you have an approximate eigenvalue you could try to find approximate eigenvectors using SVD. Last, I'm going to delete my answer because it was essentially a formatted comment and obsoleted by your edit... – gboffi Oct 27 '18 at 13:37
  • Yup, thats right. – user3419643 Oct 30 '18 at 09:11

1 Answers1

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If the determinant of a square matrix n×n A is zero, then A is not invertible. If it is not invertible there is so solution.

Ashutosh Chapagain
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  • Sometimes you have a solution ***only if the determinant of the coefficient matrix*** equals zero. Eigenvalues and eigenvectors, that is. – gboffi Oct 26 '18 at 09:20
  • Not in homogeneous case. In this case you have solutions only if det = 0. – user3419643 Oct 26 '18 at 09:48