On the Dimension of the Locus of Determinantal Hypersurfaces

Abstract

AbstractThe characteristic polynomial PA(x0 , . . . , xr) of an r-tuple A := (A1 , . . . , Ar) of n×n-matrices is defined asWe show that if r E h and A := (A1 , . . . , Ar) is an r-tuple of n × n-matrices in general position, then up to conjugacy, there are only ûnitely many r-tuples A' := (A'1 , . . . , A' r) such that pA = pA' . Equivalently, the locus of determinantal hypersurfaces of degree n in Pr is irreducible of dimension (r − 1)n2 + 1.