Timeline for Linear independence in $\mathbb{Z}_q^n$
Current License: CC BY-SA 4.0
4 events
| when toggle format | what | by | license | comment | |
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| Jun 13 at 18:20 | comment | added | Gro-Tsen | For $n=1$, there are $\varphi(q)$ elements of $\mathbb{Z}/q\mathbb{Z}$ that are (each, separately) “linearly independent”, so to find a single vector you need $q-\varphi(q)+1$ vectors. This does not bode well for your question. | |
| Jun 13 at 18:19 | comment | added | Emil Jeřábek | Generalizing your $(3,3)$ example, if $p$ is any prime divisor of $q$, then $p\mathbb Z_q^n$ is a set of $(q/p)^n$ vectors that does not contain a single linearly independent vector, according to your interpretation of the definition. Does that not answer the questin negatively? | |
| Jun 13 at 17:54 | history | edited | aleph | CC BY-SA 4.0 |
added 9 characters in body
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| Jun 13 at 14:56 | history | asked | aleph | CC BY-SA 4.0 |