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Math Help - Notation Question - Vertical Bar

  1. #1
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    [SOLVED] Notation Question - Vertical Bar

    I'm pretty sure this is a basic thing I'm just not aware of, but I can provide the whole text if necessary...(it's from a matrix-based proof for the existence of strongly regular graphs.)

    If A is a matrix and j is an eigenvector of A, what does the vertical bar in A|j^⊥ mean?

    Thanks in advance!
    Last edited by wscrosswy; April 22nd 2011 at 10:14 AM.
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  2. #2
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    The whole text surrounding the instance of the notation would be a big help (a text without a context is a pretext, for all Derrida's idiotic post-modern deconstructionism ). My guess is that the notation here means the restriction of A to the set of vectors perpendicular to j. That is, you're artificially restricting the domain of A. But I'd need to see the context in order to confirm.
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  3. #3
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    Hm, that sounds right, given the context. Here's the full text:

    Given a graph G with adjacency matrix A, G is regular if and only if the all-1 vector j is an eigenvector of A; the corresponding eigenvalue is the valency. Since is symmetric, j^⊥ is A-invariant. Then G is strongly regular if and only if A|j^⊥ has just two distinct eigenvalues. (We have already seen the 'only-if' part of this. Conversely, if (A-rho_1*I)(A-rho_2*I)|j^⊥=0, then (A-rho_1*I)(A-rho_2*I)=alpha*J for some alpha, whence A^2 (in) <I,J,A> and G is strongly regular.
    A quote that long probably deserves a citation - it's on p16 of Graph Theory, Coding Theory, and Block Designs by Cameron and Van Lint.

    PS - Please pardon my lack of LaTeX skills.
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  4. #4
    A Plied Mathematician
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    Yeah, it looks like my hunch is correct.

    Your lack of LaTeX skills is a bit academic at this point, with LaTeX not working right now, though there are work-arounds. MathGuru, the owner of the site, is, as we speak, working on restoring LaTeX, so yay!
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