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This will be a strange question: I know what to do, and I am actually doing it, and it works, but I don't know how to write about it. Looking for solutions to a homogeneous matrix equation, say AX=0, I use the kernel of the parameter matrix A. But, the world being imperfect as it is, the matrix does not have a "perfect" kernel; it does have an "imperfect" one if you set a nonzero "tolerance" parameter. FWIW I'm using Scilab, the function is kernel(A,tol).

Now what are the correct terms for "imperfect kernel", or "tolerance" (of what?), how should this whole process be described in correct English and maths terminology? Should I say something like a "least-squares kernel"? "Approximate kernel"? Is tol the "tolerance of kernel-determination algorithm"? Sounds lame to me...

Xirdal
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Depending on the method used (QR or SVD, third flag allows to choose this in Scilab implementation) the tolerance is used to determine when pivots (QR case) or singular values (SVD case) are consider to be zero. The kernel is then considered to be the associated subspace.

Stéphane Mottelet
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  • Thank you for your reply, but this is not what I was asking about. I know how it works; I do not know how to write about it in purely mathematical terms, without reference to particular software. Should I say that I find an "approximate kernel" by setting "the tolerance" to a nonzero value, or is there a more specific name for this parameter? – Xirdal Aug 23 '21 at 11:27