%0 Journal Article %T Intrinsic volumes of set of singular matrices %A Antonio Lerario %J Mathematics %D 2014 %I arXiv %X 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. %U http://arxiv.org/abs/1401.4853v1