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A Brauer's theorem and related results

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A Brauer's theorem and related results

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Bru García, R.; Cantó Colomina, R.; Soto, RL.; Urbano Salvador, AM. (2012). A Brauer's theorem and related results. Central European Journal of Mathematics. 10(1):312-321. doi:10.2478/s11533-011-0113-0

Por favor, use este identificador para citar o enlazar este ítem: http://hdl.handle.net/10251/51870

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Title: A Brauer's theorem and related results
Author:
UPV Unit: Universitat Politècnica de València. Instituto Universitario de Matemática Multidisciplinar - Institut Universitari de Matemàtica Multidisciplinària
Universitat Politècnica de València. Departamento de Matemática Aplicada - Departament de Matemàtica Aplicada
Issued date:
Abstract:
Given a square matrix A, a Brauer's theorem [Brauer A., Limits for the characteristic roots of a matrix. IV. Applications to stochastic matrices, Duke Math. J., 1952, 19(1), 75-91] shows how to modify one single eigenvalue ...[+]
Subjects: Controllability , Deflation techniques , Eigenvalues , Low rank perturbation , Pole assignment problem
Copyrigths: Reserva de todos los derechos
Source:
Central European Journal of Mathematics. (issn: 1895-1074 ) (eissn: 1644-3616 )
DOI: 10.2478/s11533-011-0113-0
Publisher:
Springer Verlag (Germany)
Publisher version: http://dx.doi.org/10.2478/s11533-011-0113-0
Thanks:
This work is supported by Fondecyt 1085125, Chile, the Spanish grant DGI MTM2010-18228 and the Programa de Apoyo a la Investigacion y Desarrollo (PAID-06-10) of the UPV.
Type: Artículo

References

Brauer A., Limits for the characteristic roots of a matrix. IV. Applications to stochastic matrices, Duke Math. J., 1952, 19(1), 75–91

Crouch P.E., Introduction to Mathematical Systems Theory, Mathematik-Arbeitspapiere, Bremen, 1988

Delchamps D.F., State-Space and Input-Output Linear Systems, Springer, New York, 1988 [+]
Brauer A., Limits for the characteristic roots of a matrix. IV. Applications to stochastic matrices, Duke Math. J., 1952, 19(1), 75–91

Crouch P.E., Introduction to Mathematical Systems Theory, Mathematik-Arbeitspapiere, Bremen, 1988

Delchamps D.F., State-Space and Input-Output Linear Systems, Springer, New York, 1988

Hautus M.L.J., Controllability and observability condition of linear autonomous systems, Nederl. Akad. Wetensch. Indag. Math., 1969, 72, 443–448

Kailath T., Linear Systems, Prentice Hall Inform. System Sci. Ser., Prentice Hall, Englewood Cliffs, 1980

Langville A.N., Meyer C.D., Deeper inside PageRank, Internet Math., 2004, 1(3), 335–380

Perfect H., Methods of constructing certain stochastic matrices. II, Duke Math. J., 1955, 22(2), 305–311

Saad Y., Numerical Methods for Large Eigenvalue Problems, Classics Appl. Math., 66, SIAM, Philadelphia, 2011

Soto R.L., Rojo O., Applications of a Brauer theorem in the nonnegative inverse eigenvalue problem, Linear Algebra Appl., 2006, 416(2–3), 844–856

Wilkinson J.H., The Algebraic Eigenvalue Problem, Clarendon Press, Oxford, 1965

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