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I'm attempting to understand a paper[1] on contracting geometry for computer graphics. I have an undergraduate Physics degrees to give some indication of my experience, though that was 6 years ago now.

I'm stumbling on a basic part as I'm unfamiliar with the notation:

$$ \begin{bmatrix} \mathbf{W}_L\mathbf{L} \\ \mathbf{W}_H \end{bmatrix}\mathbf{V}' = \begin{bmatrix} 0 \\ \mathbf{W}_H\mathbf{V} \end{bmatrix} $$

Were to blindly guess I'd suggest it was shorthand for specifying:

$$ \mathbf{W}_L\mathbf{L}\mathbf{V}' = 0 $$ and $$ \mathbf{W}_H\mathbf{V}' = \mathbf{W}_H\mathbf{V} $$

But then I'm confused by the relevance of the second equation in the context.

I don't know if I've provided enough information. Happy to provide more if desired.

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up vote 0 down vote accepted

Those square brackets are the notation for matrices. See the wikipedia article about mathematics matrix.

If you're doing computer graphics work, you should at least know some Linear Algebra, you can view a few lectures here :

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Thanks, I think I was confused by W, L & V all being matrices as well. So they're matrices of matrices? – MichaelJones Apr 14 '12 at 23:12
Sure are, they're simply block matrices. That is, the matrices are written in terms of smaller matrices. – Patrick McLaren Apr 14 '12 at 23:14
Great thanks, apparently I've not encountered block matrices before. Thanks for the link too, seems like it is time to address a gap in my knowledge. – MichaelJones Apr 14 '12 at 23:25
No problem. Since you've been through Physics, may I suggest a textbook that may be suitable, perhaps "Linear Algebra Done Right" by Axler, see . Something fun to keep around your desk, if nothing else. – Patrick McLaren Apr 14 '12 at 23:34

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