Intrinsic volumes of set of singular matrices

Abstract

We explicitly compute the intrinsic volume of the set of real (and real symmetric) matrices of Frobenius norm one and given corank (the case of matrices with zero determinant as a special case). We give asymptotic formulas for our computations and we discuss several examples and applications.

References in corpus (3)

• On the number of components of a complete intersection of real quadrics
• Complexity of intersections of real quadrics and topology of symmetric determinantal varieties
• Gap probabilities and applications to geometry and random topology