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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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1 Answer

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Those square brackets are the notation for matrices. http://en.wikipedia.org/wiki/Matrix_(mathematics)

If you're doing computer graphics work, you should at least know some Linear Algebra, you can view a few lectures here http://ocw.mit.edu/courses/mathematics/18-06-linear-algebra-spring-2010/.

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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 amzn.com/0387982582 . Something fun to keep around your desk, if nothing else. –  Patrick McLaren Apr 14 '12 at 23:34
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