On the linear capacity of algebraic cones. (English) Zbl 1007.15002

Summary: We define the linear capacity of an algebraic cone, give basic properties of the notion and new formulations of certain known results of 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.


15A03 Vector spaces, linear dependence, rank, lineability
15A63 Quadratic and bilinear forms, inner products
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