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Field now geometry. Could be also Algebra, but classified this way in anticipation of a separate Algebraic Geometry field. Stca74 06:59, 31 May 2007 (UTC) |
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Regarding the fact that matrix inversion is polynomial, wouldn't the usual Cayley-Hamilton argument make this clearer? Michael Kinyon 16:49, 11 April 2006 (UTC)
- Well, OK, I guess since Cayley-Hamilton follows from Cramer's Rule, it's not really all that different. Still, there is something about the way the argument is written here that is unsatisfactory. I just can't quite put my finger on it. Michael Kinyon 16:53, 11 April 2006 (UTC)
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- Another construction (perhaps a more natural one) interprets GL(n) as a group in 2n^2 coordinates, namely as a group of mutually inverse pairs of n by n matrices. In other words: GL(n)={(A,B)|AB=1}. Matrix inversion is just swapping coordinates and hence obviously polynomial. Lenthe 09:48, 30 November 2006 (UTC)
