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September 24, 2013, 14:54 
linear algebra question, spectral radius

#1 
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Shenren Xu
Join Date: Jan 2011
Location: London, U.K.
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Dear colleagues,
Could anyone please help me on this seemingly (maybe it in fact is) simple linear algebra problem? Suppose you have nonsingular matrices A and B, is the following true? \rho (A * B) =rho (A^T * B^T) \rho here means the spectral radius of the matrix. If so, how do I prove it mathematically? Regards, Shenren 

September 24, 2013, 15:23 

#2  
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Filippo Maria Denaro
Join Date: Jul 2010
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Quote:
I am not sure your relation is true ... I just remember that rho(A*B) <= A B where * is a matrix norm ... 

September 25, 2013, 05:18 

#3 
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Shenren Xu
Join Date: Jan 2011
Location: London, U.K.
Posts: 63
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I found the proof afterwards however, from a paper by
Prof. Mike Giles, "on the iterative solution of a discrete adjoint equation", which can be found by googling "mike giles oxford adjoint" 

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