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Results tagged with matrices
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user 2900
Questions where the notion matrix has an important or crucial role (for the latter, note the tag matrix-theory for potential use). Matrices appear in various parts of mathematics, and this tag is typically combined with other tags to make the general subject clear, such as an appropriate top-level tag ra.rings-and-algebras, co.combinatorics, etc. and other tags that might be applicable. There are also several more specialized tags concerning matrices.
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Groups of matrices that preserve several quadratic forms
Given two (or more) quadratic forms (on the same vector space) consider the group of matrices that preserve these forms, i.e. $Q_i=U Q_i U^T$, $i=1,2..,k$ What is known about such groups? …
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a generalization of the annihilator of cokernel ideal (some new invariants of modules?) [closed]
(As can be seen already for the diagonal matrices.)
For my work I need the following, "more refined" version, which follows this reducedness idea. … It seems that for square matrices $a.c._k(A)=I_k(A):I_{k-1}(A)$.
If $A=diag(\lambda_1,\dots,\lambda_m)$, with $(\lambda_1)\supseteq\cdots\supseteq(\lambda_m)$, then $a.c._k(A)=(\lambda_k)$.
$a.c. …
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the annihilator of cokernel in a particular case
Consider the $mn\times(m^2+n^2)$ matrix $A\otimes 1_{nn}\oplus 1_{mm}\otimes A^T$, here $1_{mm}$, $1_{nn}$ are identity matrices. … There are lots of tricks for computing the determinants of tricky matrices (and hence the fitting ideals) but I do not know any tricks to compute the annihilator of cokernel. Any suggestion?
upd. …
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the pfaffian-adjugate and its counterparts for matrices odd size
Still, one would like to distinguish between the generic matrices (of corank=1) and more degenerate (of corank$\ge2$). … In my case I consider the submodule $Span(UA+AU^T)\subseteq Mat(n,R)$, where $U$ runs over all the possible matrices (not necessarily skew-symmetric). …
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"embedding" various matrix equivalences into the equivalence of particular linear map
$A=UBU^T$ iff for some associated matrices $\mathcal{A,B}$ and some invertible matrices $\mathcal{U,V}$: $\mathcal{A=UBV}$) Does the congruence come from some quiver? … $A=BJac_\phi$ iff for some associated matrices $\mathcal{A,B}$ and some invertible matrices $\mathcal{U,V}$: $\mathcal{A=UBV}$). …
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