Timeline for Minimum of $\mathrm{rank}\left( \boldsymbol{W} \boldsymbol{H} \right)$, with $\boldsymbol{W}$ block diagonal
Current License: CC BY-SA 4.0
11 events
| when toggle format | what | by | license | comment | |
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| Apr 24, 2020 at 7:38 | history | edited | Juan | CC BY-SA 4.0 |
edited title
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| Apr 7, 2020 at 16:53 | history | edited | Juan |
edited tags
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| Apr 7, 2020 at 16:22 | history | edited | Juan | CC BY-SA 4.0 |
added 75 characters in body
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| Apr 7, 2020 at 14:09 | history | edited | Juan | CC BY-SA 4.0 |
Reformulated the question
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| Mar 25, 2020 at 11:39 | comment | added | Juan | That's true, but we are interested in the case where $\boldsymbol{W}$ can be constructed for each $\boldsymbol{H}$. We have edited the post accordingly to clarify this fact. Sorry for the misunderstanding. | |
| Mar 25, 2020 at 11:36 | history | edited | Juan | CC BY-SA 4.0 |
added 153 characters in body
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| Mar 24, 2020 at 19:14 | comment | added | KhashF | I think for a "generic" choice of a full rank matrix $H$, ${\rm{rank}}(WH)$ coincides with $\min\{{\rm{rank}}{W},{\rm{rank}}{H}\}$. Indeed, assuming that $m\leq k$ so that ${\rm{rank}}(H)=\min\{nl,k\}$ is not smaller than ${\rm{rank}}(W)=m$, the condition ${\rm{rank}}(WH)<m$ could be described as the vanishing of certain $m\times m$ minor. So ${\rm{rank}}(WH)=m$ for any $H$ except those belonging to a closed nowhere dense subset of positive codimension. | |
| S Mar 24, 2020 at 17:55 | history | edited | R.P. | CC BY-SA 4.0 |
Typos fixed, two new tags suggested.
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| S Mar 24, 2020 at 17:55 | history | suggested | KhashF | CC BY-SA 4.0 |
Typos fixed, two new tags suggested.
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| Mar 24, 2020 at 17:24 | review | Suggested edits | |||
| S Mar 24, 2020 at 17:55 | |||||
| Mar 24, 2020 at 17:17 | history | asked | Juan | CC BY-SA 4.0 |