Timeline for Is the number of similarity classes of integer matrices with given minimal and characteristic polynomial finite?
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| Nov 19 at 17:53 | comment | added | Henri Johnston | You can also show one direction of the implication another way. Curtis and Reiner, Methods of Representation Theory, Volume 1, Proposition (24.4) implies that if $\Lambda$ is a $\mathbb{Z}$-order in a finite-dimensional non-semisimple $\mathbb{Q}$-algebra $A$, then there are infinitely many distinct isomorphism classes of $\Lambda$-lattices in $A$. Under the correspondence with modules/lattices in the reference I gave above, it then follows that a non-semisimple matrix $M$ has infinitely many non-similar matrices with the same minimal and characteristic polynomials as $M$. | |
| S Nov 16 at 1:57 | review | First answers | |||
| Nov 16 at 2:12 | |||||
| S Nov 16 at 1:57 | history | answered | Ben Marlin | CC BY-SA 4.0 |