An envelope for the spectrum of a matrix

• Autorzy: Panayiotis Psarrakos , Michael Tsatsomeros
• Języki publikacji: EN

Abstrakty

EN

We introduce and study an envelope-type region ɛ(A) in the complex plane that contains the eigenvalues of a given n×n complex matrix A. ɛ(A) is the intersection of an infinite number of regions defined by cubic curves. The notion and method of construction of ɛ(A) extend the notion of the numerical range of A, F(A), which is known to be an intersection of an infinite number of half-planes; as a consequence, ɛ(A) is contained in F(A) and represents an improvement in localizing the spectrum of A.

Słowa kluczowe

EN

Eigenvalue bounds; Numerical range; Cubic curve

Kategorie tematyczne

• 15A60: Norms of matrices, numerical range, applications of functional analysis to matrix theory
• 15A18: Eigenvalues, singular values, and eigenvectors

• Wydawca: De Gruyter Open
• Czasopismo: Open Mathematics
• Rocznik: 2012
• Tom: 10
• Numer: 1
• Strony: 292-302

Daty

wydano

2012-02-01

online

2011-12-09

Twórcy

autor

Panayiotis Psarrakos

• National Technical University of Athens

autor

Michael Tsatsomeros

• Washington State University

Bibliografia

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• [2] Brown E.S., Spitkovsky I.M., On flat portions on the boundary of the numerical range, Linear Algebra Appl., 2004, 390, 75–109 http://dx.doi.org/10.1016/j.laa.2004.04.009
• [3] Horn R.A., Johnson C.R., Topics in Matrix Analysis, Cambridge University Press, Cambridge, 1991 http://dx.doi.org/10.1017/CBO9780511840371
• [4] Johnson C.R., Numerical determination of the field of values of a general complex matrix, SIAM J. Numer. Anal., 1978, 15(3), 595–602 http://dx.doi.org/10.1137/0715039
• [5] Levinger B.W., An inequality for nonnegative matrices, Notices Amer. Math. Soc., 1970, 17, 260
• [6] McDonald J.J., Psarrakos P.J., Tsatsomeros M.J., Almost skew-symmetric matrices, Rocky Mountain J. Math., 2004, 34(1), 269–288
• [7] Milne J.S., Elliptic Curves, BookSurge, Charleston, 2006
• [8] Psarrakos P.J., Tsatsomeros M.J., Bounds for Levinger’s function of nonnegative almost skew-symmetric matrices, Linear Algebra Appl., 2006, 416, 759–772 http://dx.doi.org/10.1016/j.laa.2005.12.018
• [9] Tretter C., Spectral Theory of Block Operator Matrices and Applications, Imperial College Press, London, 2008 http://dx.doi.org/10.1142/9781848161122
• [10] Tretter C., Wagenhofer M., The block numerical range of an n×n block operator matrix, SIAM J. Matrix Anal. Appl., 2003, 24(4), 1003–1017 http://dx.doi.org/10.1137/S0895479801394076

Identyfikatory

DOI

10.2478/s11533-011-0111-2