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My goal is to compute the normal vectors of hyperplane, for which an explanation can be found in the answers of this post. For this I have written Gaussian elimination algorithms to convert the matrix to both row-echelon form and reduced row-echelon form. From my understanding the null space can be directly obtained from its RREF.

However, I have difficulties finding a resource that explains how to extract the null space algorithmically from either REF or RREF. The solution seems to involve writing down a system of linear equations in the later steps, which is useful for solving it manually, but not programmatically.

I am sure the answer to this problem is simple and I am just missing something. If someone knows which algorithm can obtain the null space from RREF or REF or knows the general steps required to implement one, it would be greatly appreciated.

Ood
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    How do you want the null space described? E.g. this gives a procedure that is perfectly implementable as an algorithm. – Jakob Streipel Mar 09 '24 at 15:43
  • @JakobStreipel Thank you, that answer may be helpful. Given that I am trying to compute the normals, I am assuming it should be described as a series of vectors, which are orthogonal to the hyperplane. – Ood Mar 09 '24 at 15:59

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