Timeline for Can we recover all $k$-minors of a square matrix from some of them?
Current License: CC BY-SA 4.0
4 events
| when toggle format | what | by | license | comment | |
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| Dec 11, 2019 at 14:48 | comment | added | Asaf Shachar | Thank you. I am merely curious. Perhaps there is a structural way to simplify this "computational search", but I don't see such a thing at the moment... | |
| Dec 11, 2019 at 14:45 | comment | added | Arnaud Mortier | @AsafShachar To obtain a more explicit statement, one would need to take a closer look at the list of polynomials, which can be a huge task depending on $k$ and $n$. I'll see what this gives in small examples when I have more time. | |
| Dec 11, 2019 at 14:17 | comment | added | Asaf Shachar | Thank you! Can you elaborate on what do you mean "by practice, it means that there is some maximal number of $k$-minors that can be fixed independently, after which all the others will be uniquely determined by the equations"? Do you have a more precise statement? e.g. can you say how many minors will be needed to determine all the rest? (say for an invertible matrix). Can we describe an explicit choice of a subset of the minors that will suffice? | |
| Dec 11, 2019 at 8:37 | history | answered | Arnaud Mortier | CC BY-SA 4.0 |