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

#1 
Member
Shenren Xu
Join Date: Jan 2011
Location: London, U.K.
Posts: 63
Rep Power: 6 
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  
Senior Member
Filippo Maria Denaro
Join Date: Jul 2010
Posts: 1,863
Rep Power: 25 
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 
Member
Shenren Xu
Join Date: Jan 2011
Location: London, U.K.
Posts: 63
Rep Power: 6 
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" 

Thread Tools  
Display Modes  


Similar Threads  
Thread  Thread Starter  Forum  Replies  Last Post 
about convergence of a linear system  harbinyg  Main CFD Forum  2  June 22, 2011 06:22 
spectral radius R  wxm  Main CFD Forum  0  August 6, 2006 02:33 
comments on FDM, FEM, FVM, SM, SEM, DSEM, BEM  kenn  Main CFD Forum  2  July 18, 2004 18:28 
Spectral Vs FEM  Khurram  Main CFD Forum  0  December 15, 2002 18:33 
FEM/Linear algebra question  clifford bradford  Main CFD Forum  7  May 4, 2001 23:47 