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eigenvalues of the product of two matrices

  • To: mathgroup at smc.vnet.net
  • Subject: [mg38074] eigenvalues of the product of two matrices
  • From: "Kumar Chellapilla" <kumarc at microsoft.com>
  • Date: Thu, 28 Nov 2002 14:10:05 -0500 (EST)
  • Sender: owner-wri-mathgroup at wolfram.com

Hi everyone,

Given
            C = A*B,
where A, B, and C are n x n matrices,
and * represents a matrix product, I am looking for
pointers on how the eigen values of  C are related to
those of A and B.

If necessary, I also know that A and B are
real, non-negative, and stochastic.

We do know that, for
            C = A*A = A^2
eig(C) = eig(A)^2 (elementwise)

Thank you,
Kumar





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