Timeline for The multiplicity of the max eigenvalue in matrix multiplication
Current License: CC BY-SA 3.0
5 events
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| May 25, 2014 at 18:22 | comment | added | Misha | @FelixGoldberg: One rewrites PMP (for 3 matrices) as $C=AB$. There is no assumption in PMP for all eigenvalues to be 1. Of course, PMP is much more general than the one in OP's question. My point was to show that there are nontrivial restrictions on the eigenvalues of the products of matrices (which was part 1 of the OP's question). I did not think about the question 2 (and did not think about this question at all since 2 years ago). | |
| May 25, 2014 at 8:36 | comment | added | Felix Goldberg | I must be missing something, but isn't the PMP more complicated than what the OP asked for? His question (1) asks for positive eigenvalues, whereas PMP apparently forces them all to be 1. His question (2) only refers to the largest eigenvalue. So - what have I missed? Thanks! | |
| Mar 7, 2012 at 20:14 | history | edited | Misha | CC BY-SA 3.0 |
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| Mar 5, 2012 at 17:07 | comment | added | Igor Rivin | This is an excellent answer, however, the reference seems to be rather opaque, and in particular, I am having trouble deducing any sort of answer to the OP's question from this (the very last theorem in the paper seems relevant, but it seems to be stated on the Lie algebra level, and I am not sure quite what to make of it). Perhaps you can clarify? | |
| Mar 5, 2012 at 17:01 | history | answered | Misha | CC BY-SA 3.0 |