Dana, M.; Ikramov, Kh. D. On the codimension of the variety of symmetric matrices with multiple eigenvalues. (Russian, English) Zbl 1081.15526 Zap. Nauchn. Semin. POMI 323, 34-46 (2005); translation in J. Math. Sci., New York 137, No. 3, 4780-4786 (2007). Summary: According to a result of Wigner and von Neumann, the dimension of the set \({\mathcal M}\) of \(n\times n\) real symmetric matrices with multiple eigenvalues is equal to \(N- 2\), where \(N= n(n+ 1)/2\). This value is determined by counting the number of free parameters in the spectral decomposition of a matrix. We show that the same dimension is obtained if \({\mathcal M}\) is interpreted as an algebraic variety. Cited in 7 Documents MSC: 15A30 Algebraic systems of matrices 15A18 Eigenvalues, singular values, and eigenvectors Keywords:codimension; variety of symmetric matrices; multiple eigenvalues; spectral decomposition PDFBibTeX XMLCite \textit{M. Dana} and \textit{Kh. D. Ikramov}, Zap. Nauchn. Semin. POMI 323, 34--46 (2005; Zbl 1081.15526); translation in J. Math. Sci., New York 137, No. 3, 4780--4786 (2007) Full Text: EuDML Link