MATHEMATICA BOHEMICA, Vol. 127, No. 3, pp. 453-462 (2002)

On the linear capacity of algebraic cones

Marcin Skrzynski

Marcin Skrzynski, Institute of Mathematics, Cracow University of Technology, ul. Warszawska 24, PL 31-155 Krakow, e-mail: skrzynsk@im.uj.edu.pl

Abstract: 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.

Keywords: irreducible algebraic cone, linear subspace, conjugacy class of a matrix, quadratic form

Classification (MSC2000): 15A63, 15A99

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