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Results tagged with matrices
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user 4096
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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Detecting if a polynomial is a Pfaffian
Given an explicit polynomial, is there any kind of trick/algorithm to check whether it is a pfaffian of a matrix with linear entries?
The pfaffian can be defined as $\sqrt{{\rm det}(A) } $ when $A$ …
- 3,779
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dimensions of strata of Pfaffian varieties
Let us consider $W=\wedge^2V$ and the Pfaffian variety $Pf\subset \mathbb{P}W$ that parametrize degenerate skew-symmetric matrices. $Pf$ is naturally stratified by the (even) rank of the matrices. … $Pf$ is the locus of rank at most $2n-2$, the singular locus $Sing(Pf)$ is the locus of rank at most $2n-4$, etc. down to the smallest stratum, which is the Grassmannian $Gr(2,2n)$, that parametrizes matrices …
- 3,779