Timeline for Relation between nullspace and row-equivalence of matrices over $\mathbb{Z}$ and $\frac{\mathbb{Z}}{n \mathbb{Z}}$?
Current License: CC BY-SA 4.0
7 events
| when toggle format | what | by | license | comment | |
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| Mar 29 at 9:03 | comment | added | Igor Khavkine | For completeness, the analog of the Hermite normal form over the integers is the Howell normal form over $\mathbb{Z}/n\mathbb{Z}$. | |
| Mar 29 at 6:39 | comment | added | Emil Jeřábek | Row operations over $\mathbb Z$ give you the Hermite normal form. | |
| Mar 28 at 20:55 | comment | added | Igor Khavkine | Over $\mathbb{Z}$, having the same kernel is weaker. For instance, take one integer matrix, and multiply it by any number that is not $0$ or $1$. The kernel remains the same, but the two matrices are no longer row equivalent. | |
| Mar 28 at 16:18 | history | edited | José | CC BY-SA 4.0 |
changed notation from Z_n to Z/(n Z)
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| Mar 28 at 9:58 | comment | added | YCor | $\mathbb{Z}_p$ usually refers to $p$-adic numbers. Please be explicit on your notation. | |
| Mar 28 at 0:46 | comment | added | José | The elementary row operation of multiplication by a constant must be by a unit in $\mathbb{Z}_n$ otherwise the operation won't be invertible. I have no idea if defining row equivalence with this constraint to row operations would still be equivalent to defining row equivalence as just having the same row-space. | |
| Mar 28 at 0:24 | history | asked | José | CC BY-SA 4.0 |