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September 24, 2013, 15:54 |
linear algebra question, spectral radius
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#1 |
Member
Shenren Xu
Join Date: Jan 2011
Location: London, U.K.
Posts: 67
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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 non-singular 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 |
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September 24, 2013, 16:23 |
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#2 | |
Senior Member
Filippo Maria Denaro
Join Date: Jul 2010
Posts: 6,760
Rep Power: 71 |
Quote:
I am not sure your relation is true ... I just remember that rho(A*B) <= ||A|| ||B|| where ||*|| is a matrix norm ... |
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September 25, 2013, 06:18 |
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#3 |
Member
Shenren Xu
Join Date: Jan 2011
Location: London, U.K.
Posts: 67
Rep Power: 15 |
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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