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Re: A * x = 0 for singular matrix


From: Quentin Spencer
Subject: Re: A * x = 0 for singular matrix
Date: Fri, 23 Feb 2007 20:47:45 -0600
User-agent: Thunderbird 1.5.0.9 (Windows/20061207)

lipschitz82 wrote:
By ~= 0 I mean approximately singular. It is singular up to my level of tolerance.

Thanks for the suggestion,
G.R.

On 2/23/07, *Quentin Spencer* <address@hidden <mailto:address@hidden>> wrote:

    lipschitz82 wrote:
    > I need to calculate the vector s.t. Ax = 0, for det(A) ~= 0. I've
    > looked at the documentation, octave-forge, etc. but I couldn't
    find a
    > routine for doing this. Matrix A is pretty big, ie. in the
    hundreds,
    > but I also have a lot of computer time if the available routine
    is slow.

    Your subject line says A is singular, but your description of the
    problem says det(A)~=0, which means it is not singular, so which
    is it?
    Assuming A is singular, the "null" function will compute a set of
    basis
    vectors for the null space of A.

    Quentin



Well, if it's nearly but not exactly singular, then I would think the best solution is to compuate a singular value decomposition (see the svd function) and choose the singular vector corresponding to the smallest singular value.
Quentin



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