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Dec 6, 2016 at 15:09 comment added Federico Poloni Note that you can prove the nonsingularity of a Vandermonde matrix with different nodes very simply without speaking about determinants --- it's basically equivalent to the fact that a nonzero degree-$d$ polynomial has at most $d$ roots.
Aug 18, 2010 at 23:16 comment added J. M. isn't a mathematician Generally determinants of structured matrices have nice structure themselves, which is one explanation for their utility.
Aug 18, 2010 at 22:33 history answered Pace Nielsen CC BY-SA 2.5