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