Timeline for A question on vectors in $\mathbb{R}^4$
Current License: CC BY-SA 4.0
6 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Oct 10, 2021 at 21:51 | answer | added | Michael Engelhardt | timeline score: 1 | |
| Oct 10, 2021 at 21:27 | comment | added | LSpice | OK, thanks. So you have fixed such an $M$, and are seeking to describe the set of all $(\mathbf u, \mathbf v)$? | |
| Oct 10, 2021 at 21:16 | history | edited | Stanley Yao Xiao | CC BY-SA 4.0 |
added 210 characters in body
|
| Oct 10, 2021 at 20:56 | comment | added | Stanley Yao Xiao | @LSpice Your concerns are valid, and in my case of interest the $M$ will be "generic" in the sense that both conditions on $\mathbf{u}, \mathbf{v}$ do occur generically. I will modify the question to include this assumption | |
| Oct 10, 2021 at 20:44 | comment | added | LSpice | Since you have already fixed $M$, "Generically, $\mathcal M$ will be invertible" seems to mean "generically in $(\mathbf u, \mathbf v)$", but that can be false, so I guess it means "generically in $(M, \mathbf u, \mathbf v)$". Similarly, read literally, "there exist pairs $\mathbf u$, $\mathbf v$ such that $\mathcal M$ has rank three" can be false; so probably it should be "there exists $(M, \mathbf u, \mathbf v)$ such that …". Because of these concerns, I am confused about what set is "the set" that you are describing linearly. Is it a set of triples or of pairs? | |
| Oct 10, 2021 at 20:34 | history | asked | Stanley Yao Xiao | CC BY-SA 4.0 |