Jonker, P.; Pouw, M.; Still, G.; Twilt, F. On the partition of real skew-symmetric \(n\times n\)-matrices according to the multiplicities of their eigenvalues. (English) Zbl 0971.58005 Butzer, P. L. (ed.) et al., Karl der Große und sein Nachwirken. 1200 Jahre Kultur und Wissenschaft in Europa. Band 2: Mathematisches Wissen. Turnhout: Brepols. 439-454 (1998). The main result of this paper is the following: Let \(A_n\) be the space of all skew-symmetric real \(n\times n\) matrices. Given a tuple \((m_0,\dots,m_k)\) of integers with \(m_0\geq 0\), \(m_1,\dots, m_k\geq 1\) and with \(n=m_0+2m_1+\cdots 2m_k\), let \(A_{m_0,m_1,\dots,m_k}\) be the set of all skew-symmetric matrices such that \(0\) is an \(m_0\)-fold eigenvalue, and which have \(2r\) distinct other eigenvalues in pairs \((i\lambda_r,-i\lambda_r)\) with multiplicity \(m_r\). Then the \(A_{m_0,\dots,m_k}\) form a Whitney regular stratification of \(A_n\), and the codimension of the stratum \(A_{m_0,\dots,m_k}\) is \(m_0(m_0-1) + \sum_{r=1}^k (m_r^2-1)\). Thom’s transversality theorem is applied to this theorem to get information about generic parameter dependent families of skew-adjoint matrices, with applications to control theory.For the entire collection see [Zbl 0942.00019]. Reviewer: Thomas Schick (Münster) Cited in 1 Document MSC: 58A35 Stratified sets 57Q65 General position and transversality 65H17 Numerical solution of nonlinear eigenvalue and eigenvector problems 93B05 Controllability Keywords:Whitney stratification; parameter families of matrices; eigenvalue perturbations; controllability of linear systems PDFBibTeX XMLCite \textit{P. Jonker} et al., in: Karl der Grosse und sein Nachwirken. 1200 Jahre Kultur und Wissenschaft in Europa. Band 2: Mathematisches Wissen. Turnhout: Brepols. 439--454 (1998; Zbl 0971.58005)