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- W2912583945 abstract "Given two $left( n+1right) timesleft( n+1right)$-matrices $A$ and $B$ over a commutative ring, and some $kinleft{ 0,1,ldots,nright}$, we consider the $dbinom{n}{k}timesdbinom{n}{k}$-matrix $W$ whose entries are $left( k+1right) timesleft( k+1right)$-minors of $A$ multiplied by corresponding $left( k+1right) timesleft( k+1right)$-minors of $B$. Here we require the minors to use the last row and the last column (which is why we obtain an $dbinom{n}{k}timesdbinom{n}{k}$-matrix, not an $dbinom{n+1}{k+1}timesdbinom{n+1}{k+1}$-matrix). We prove that the determinant $det W$ is a multiple of $det A$ if the $left( n+1,n+1right)$-th entry of $B$ is $0$. Furthermore, if the $left( n+1,n+1right)$-th entries of both $A$ and $B$ are $0$, then $det W$ is a multiple of $left( det Aright) left( det Bright)$. This extends a previous result of Olver and the author ( arXiv:1802.02900 )." @default.
- W2912583945 created "2019-02-21" @default.
- W2912583945 creator A5074897310 @default.
- W2912583945 date "2021-11-18" @default.
- W2912583945 modified "2023-09-27" @default.
- W2912583945 title "A double Sylvester determinant" @default.
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- W2912583945 doi "https://doi.org/10.26493/1855-3974.2248.d3f" @default.
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