Timeline for Expressing a polynomial as the determinant of a matrix of linear forms
Current License: CC BY-SA 4.0
9 events
| when toggle format | what | by | license | comment | |
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| Mar 15, 2021 at 20:08 | comment | added | Asvin | I found a few other references in the meanwhile. math.ucsd.edu/~helton/BILLSPAPERSscanned/HMV06.pdf and hal.archives-ouvertes.fr/file/index/docid/275615/filename/… for instance. The first 3 slides of this services.math.duke.edu/~dasgupta/Transcendence/… also contain a very understandable proof of the claim @Malkoun | |
| Mar 15, 2021 at 13:47 | comment | added | Malkoun | I asked a related question yesterday <math.stackexchange.com/questions/4060886/…>. I have also stumbled on the paper that @VladMatei provided a link to. | |
| Mar 4, 2021 at 19:35 | comment | added | Zach Teitler | Maybe a smaller but more definite question to start with is to characterize which matrices of polynomials can be realized as adjugates of matrices with linear entries, or matrix of $k$-minors ($k$-wedge) of a matrix with linear entries. Of course the size is $\binom{m}{k}\times\binom{n}{k}$, the entries have degree $k$, and the determinant of an adjugate is a pure power, but surely there are more conditions. | |
| Mar 4, 2021 at 18:22 | comment | added | Asvin | @VladMatei Thank you! I am still interested in the broader question of finding an appropriate quasi-determinant, however. | |
| Mar 4, 2021 at 18:01 | comment | added | Vlad Matei | This paper seems to contain the desired algorithm arxiv.org/ftp/arxiv/papers/1804/1804.00145.pdf | |
| Mar 4, 2021 at 17:15 | history | edited | Asvin | CC BY-SA 4.0 |
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| Mar 4, 2021 at 16:51 | comment | added | Asvin | I don't particulary care about the sizes but I heard that the result proves an exponential blowup on the sizes (wrt n). | |
| Mar 4, 2021 at 16:50 | comment | added | David E Speyer | Are there any restrictions on the sizes of the matrices $M_j$? | |
| Mar 4, 2021 at 16:48 | history | asked | Asvin | CC BY-SA 4.0 |