# Thread: Notation Question - Vertical Bar

1. ## [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?

2. 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.

3. 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.

4. 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!