On the Eigenvalues and Eigenvectors of a Class of Matrices

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Previous article Next article On the Eigenvalues and Eigenvectors of a Class of MatricesS. ParterS. Parterhttps://doi.org/10.1137/0108024PDFPDF PLUSBibTexSections ToolsAdd to favoritesExport CitationTrack CitationsEmail SectionsAbout[1] Wallace Givens, A method of computing eigenvalues and eigenvectors suggested by classical results on symmetric matricesSimultaneous linear equations and the determination of eigenvalues, National Bureau of Standards Applied Mathematics Series, No. 29, U. S. Government Printing Office, Washington, D. C., 1953, 117–122 MR0059070 0052.35003 Google Scholar[2] Karl Goldberg, A matrix with real characteristic roots, J. Res. Nat. Bur. Standards, 56 (1956), 87– MR0077490 0074.25402 CrossrefISIGoogle Scholar[3] Karl Goldberg, Random notes on matrices, J. Res. Nat. Bur. Standards, 60 (1958), 321–325 MR0092756 0089.00901 CrossrefISIGoogle Scholar[4] John Z. Hearon, The kinetics of linear systems with special reference to periodic reactions, Bull. Math. Biophys., 15 (1953), 121–141 MR0054807 CrossrefGoogle Scholar[5] Dénes König, Theorie der endlichen und unendlichen Graphen. Kombinatorische Topologie der Streckenkomplexe, Chelsea Publishing Co., New York, N. Y., 1950ix+258 MR0036989 0040.10303 Google Scholar[6] Alston S. Householder and , C. W. Sheppard, The mathematical basis of the interpretation of tracer experiments in closed steady-state systems, J. Appl. Phys., 22 (1951), 510–520 10.1063/1.1699992 MR0041411 0043.43302 CrossrefISIGoogle Scholar[7] David Rosenblatt, On linear models and the graphs of Minkowski-Leontief matrices, Econometrica, 25 (1957), 325–338 MR0089085 0086.13704 CrossrefISIGoogle Scholar[8] K. Symanzik, Dispersion relations and vertex properties in perturbation theory, Progr. Theoret. Phys., 20 (1958), 690–702 10.1143/PTP.20.690 MR0103065 0084.45002 CrossrefISIGoogle Scholar Previous article Next article FiguresRelatedReferencesCited ByDetails The Number of Interlacing Equalities Resulting from Removal of a Vertex from a TreeSIAM Journal on Discrete Mathematics, Vol. 29, No. 3 | 30 July 2015AbstractPDF (351 KB)Interlacing Properties for Hermitian Matrices Whose Graph is a Given TreeSIAM Journal on Matrix Analysis and Applications, Vol. 27, No. 1 | 31 July 2006AbstractPDF (145 KB)Hermitian Matrices, Eigenvalue Multiplicities, and Eigenvector ComponentsSIAM Journal on Matrix Analysis and Applications, Vol. 26, No. 2 | 31 July 2006AbstractPDF (147 KB)The Parter--Wiener Theorem: Refinement and GeneralizationSIAM Journal on Matrix Analysis and Applications, Vol. 25, No. 2 | 31 July 2006AbstractPDF (138 KB)Eigenvalues of a Tri-Diagonal Matrix (D. K. Ross)SIAM Review, Vol. 23, No. 1 | 17 February 2012PDF (164 KB)Qualitative Problems in Matrix TheorySIAM Review, Vol. 11, No. 1 | 17 February 2012AbstractPDF (2334 KB) Volume 8, Issue 2| 1960Journal of the Society for Industrial and Applied Mathematics225-424 History Submitted:03 September 1958Published online:10 July 2006 InformationCopyright © 1960 Society for Industrial and Applied MathematicsPDF Download Article & Publication DataArticle DOI:10.1137/0108024Article page range:pp. 376-388ISSN (print):0368-4245ISSN (online):2168-3484Publisher:Society for Industrial and Applied Mathematics