Some Elementary Properties of Proper Values and Proper Vectors of Matrix Functions

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Next article Some Elementary Properties of Proper Values and Proper Vectors of Matrix FunctionsWilliam T. ReidWilliam T. Reidhttps://doi.org/10.1137/0118021PDFBibTexSections ToolsAdd to favoritesExport CitationTrack CitationsEmail SectionsAbout[1] Lawrence M. Graves, Some general approximation theorems, Ann. of Math. (2), 42 (1941), 281–292 MR0003274 (2,193a) 0024.30701 CrossrefGoogle Scholar[2] Einar Hille and , Ralph S. Phillips, Functional analysis and semi-groups, American Mathematical Society Colloquium Publications, vol. 31, American Mathematical Society, Providence, R. I., 1957xii+808 MR0089373 (19,664d) 0078.10004 Google Scholar[3] E. W. Hobson, The Theory of Functions of a Real Variable and the Theory of Fourier Series, Vol. 1, Harren Press, Washington, D.C., 1950 Google Scholar[4] Tosio Kato, Perturbation theory for linear operators, Die Grundlehren der mathematischen Wissenschaften, Band 132, Springer-Verlag New York, Inc., New York, 1966xix+592 MR0203473 (34:3324) 0148.12601 CrossrefGoogle Scholar[5] William T. Reid, A Prüfer transformation for differential systems, Pacific J. Math., 8 (1958), 575–584 MR0099474 (20:5913) 0102.30004 CrossrefGoogle Scholar[6] William T. Reid, Properties of solutions of a Riccati matrix diferential equation, J. Math. Mech., 9 (1960), 749–770 MR0123779 (23:A1101) 0119.29901 ISIGoogle Scholar[7] William T. Reid, Variational methods and boundary problems for ordinary linear differential systems, Proc. U.S.-Japan Seminar on Differential and Functional Equations (Minneapolis, Minn., 1967), Benjamin, New York, 1967, 267–299 MR0228743 (37:4322) 0178.09102 Google Scholar[8] Franz Rellich, Störungstheorie der Spektralzerlegung, Math. Ann., 113 (1937), 600–619 10.1007/BF01571652 MR1513109 0016.06301 CrossrefGoogle Scholar Next article FiguresRelatedReferencesCited byDetails On Various Levels of Linear Independence for Integer Translates of a Finite Number of Functions3 June 2015 Cross Ref Bibliography23 May 2013 Cross Ref Control of nonlinear delay differential equations in W2(1) with economic applicationsApplied Mathematics and Computation, Vol. 85, No. 1 Cross Ref Target path controllability of linear time-varying dynamical systemsIEEE Transactions on Automatic Control, Vol. 30, No. 1 Cross Ref The existence of periodic solutions for nonlinearly perturbed conservative systemsNonlinear Analysis: Theory, Methods & Applications, Vol. 3, No. 5 Cross Ref Optimal Control of Functional Differential SystemsF. Colonius and D. Hinrichsen1 August 2006 | SIAM Journal on Control and Optimization, Vol. 16, No. 6AbstractPDF (1960 KB)Interrelations between a trace formula and Liapunov type inequalitiesJournal of Differential Equations, Vol. 23, No. 3 Cross Ref Principal quadratic functionals1 January 1976 | Transactions of the American Mathematical Society, Vol. 218, No. 0 Cross Ref Characterization of the Controlled States in $W_2^{(1)} $ of Linear Hereditary SystemsH. T. Banks, Marc Q. Jacobs, and C. E. Langenhop18 July 2006 | SIAM Journal on Control, Vol. 13, No. 3AbstractPDF (3182 KB)Admissibility and integral operatorsMathematical Systems Theory, Vol. 7, No. 3 Cross Ref An optimum settling problem for time lag systesmJournal of Mathematical Analysis and Applications, Vol. 40, No. 3 Cross Ref References Cross Ref A matrix Liapunov inequalityJournal of Mathematical Analysis and Applications, Vol. 32, No. 2 Cross Ref Volume 18, Issue 2| 1970SIAM Journal on Applied Mathematics History Submitted:11 February 1969Published online:01 August 2006 InformationCopyright © 1970 © Society for Industrial and Applied MathematicsPDF Download Article & Publication DataArticle DOI:10.1137/0118021Article page range:pp. 259-266ISSN (print):0036-1399ISSN (online):1095-712XPublisher:Society for Industrial and Applied Mathematics