Linear algebra nugget of the day. You can classify a 2d quadratic form without finding eigenvalues. Det tells you if the eigenvalues are the same sign and if det is positive, trace tells you which sign. Exercise: what if det is 0?
There's nothing wrong with assuming anything you like, but it's mildly bad not to mention what you're assuming.
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Can't disagree with that. Been spending to much time taking an inner product for granted recently. I'm a mildly bad person :-)
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Well, prolonged experience working in general relativity theory tends to do this to a man. I sympathize; the metric in GR is so profound and omnipresent a structure that one tends to forget what it's like not to have one.
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