Compactness

March 14th, 2008 ~ Posted in: Mathematics

Here’s an interesting question:

Let G = \{ A \,:\, A^T S A = S \} where S = \begin{matrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & -2 \end{matrix}. Is G compact?

I won’t say where this problem came from, in the interest of making it a little harder, but I will say that I couldn’t solve it (in my defense, I didn’t try very hard :) ). However, someone did show me a really elegant solution…

Mathematics ~

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