Timeline for Growth of an integer vector under the action of a matrix in $GL_n(\mathbb{Z})$
Current License: CC BY-SA 3.0
5 events
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| Feb 28 at 18:11 | comment | added | YCor | @ghc1997 Yes, it's true (nothing to do with $\mathbf{Z}$: it's true for $A\in\mathrm{GL}_n(\mathbf{Q})$). Just consider kernel and image of $(A^{k!}-1)^n$ for large enough $k$. | |
| Feb 28 at 18:01 | comment | added | ghc1997 | Hi Yves, I have a slightly related question. Let $A\in\mathrm{GL}_n(\mathbf{Z})$, if we denote $V_{\mathrm{nru}} $ to be the sum of characteristic subspaces of $A$ relative to eigenvalues that are not roots of unity. Can we always find a basis of $V_{\mathrm{nru}} $ in $\mathbf{Q}^n $, i.e. do we have $\mathrm{dim} V_{\mathrm{nru}} =\mathrm{dim} V_{\mathrm{nru}} \cap\mathbf{Q}^n$? | |
| Feb 16, 2016 at 15:09 | vote | accept | Lee Mosher | ||
| Feb 16, 2016 at 7:43 | history | edited | YCor | CC BY-SA 3.0 |
Added additional argument
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| Feb 15, 2016 at 23:22 | history | answered | YCor | CC BY-SA 3.0 |