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Start Over Creator Skrzyński, Marcin

1. Irreducible algebraic sets of matrices with dominant restriction of the characteristic map

Creator:
Skrzyński, Marcin
Format:
bez média and svazek
Type:
model:article and TEXT
Subject:
characteristic map, dominant map, linear subspace, GLn-invariant set of matrices, and rank variet
Language:
English
Description:
We collect certain useful lemmas concerning the characteristic map, GLninvariant sets of matrices, and the relative codimension. We provide a characterization of rank varieties in terms of the characteristic map as well as some necessary and some sufficient conditions for linear subspaces to allow the dominant restriction of the characteristic map.
Rights:
http://creativecommons.org/publicdomain/mark/1.0/ and policy:public

2. On the linear capacity of algebraic cones

Creator:
Skrzyński, Marcin
Format:
bez média and svazek
Type:
model:article and TEXT
Subject:
irreducible algebraic cone, linear subspace, conjugacy class of a matrix, and quadratic form
Language:
English
Description:
We define the linear capacity of an algebraic cone, give basic properties of the notion and new formulations of certain known results of the Matrix Theory. We derive in an explicit way the formula for the linear capacity of an irreducible component of the zero cone of a quadratic form over an algebraically closed field. We also give a formula for the linear capacity of the cone over the conjugacy class of a ''generic'' non-nilpotent matrix.
Rights:
http://creativecommons.org/publicdomain/mark/1.0/ and policy:public