Actually, as Victor pointed out earlier, Wikipedia did know this, but in an obscure entry far from the discussion of matrices. It is not attributed to Krylov, however. http://en.wikipedia.org/wiki/Newton%27s_identities "The Newton identities now relate the traces of the powers A^k to the coefficients of the characteristic polynomial of A. Using them in reverse to express the elementary symmetric polynomials in terms of the power sums, they can be used to find the characteristic polynomial by computing only the powers A^k and their traces." At 11:43 AM 12/3/2009, mcintosh@servidor.unam.mx wrote:
Quoting Henry Baker <hbaker1@pipeline.com>:
I noticed in Wikipedia's description of eigenvalues, an expansion of the characteristic polynomial of a 3x3 matrix in terms of traces, so I wanted to see if this worked more generally.
It looks like you may have noticed Newton's identities, and thereby Krylov's method of getting characteristic equations.
Wikipedia, much less God, doesn't know everything.
-hvm
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