An envelope for the spectrum of a matrix
Panayiotis Psarrakos; Michael Tsatsomeros
Open Mathematics (2012)
- Volume: 10, Issue: 1, page 292-302
- ISSN: 2391-5455
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topPanayiotis Psarrakos, and Michael Tsatsomeros. "An envelope for the spectrum of a matrix." Open Mathematics 10.1 (2012): 292-302. <http://eudml.org/doc/269630>.
@article{PanayiotisPsarrakos2012,
abstract = {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.},
author = {Panayiotis Psarrakos, Michael Tsatsomeros},
journal = {Open Mathematics},
keywords = {Eigenvalue bounds; Numerical range; Cubic curve; eigenvalue bounds; numerical range; cubic curve; spectrum},
language = {eng},
number = {1},
pages = {292-302},
title = {An envelope for the spectrum of a matrix},
url = {http://eudml.org/doc/269630},
volume = {10},
year = {2012},
}
TY - JOUR
AU - Panayiotis Psarrakos
AU - Michael Tsatsomeros
TI - An envelope for the spectrum of a matrix
JO - Open Mathematics
PY - 2012
VL - 10
IS - 1
SP - 292
EP - 302
AB - 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.
LA - eng
KW - Eigenvalue bounds; Numerical range; Cubic curve; eigenvalue bounds; numerical range; cubic curve; spectrum
UR - http://eudml.org/doc/269630
ER -
References
top- [1] Adam M., Tsatsomeros M.J., An eigenvalue inequality and spectrum localization for complex matrices, Electron. J. Linear Algebra, 2006, 15, 239–250 Zbl1142.15305
- [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 Zbl1059.15031
- [3] Horn R.A., Johnson C.R., Topics in Matrix Analysis, Cambridge University Press, Cambridge, 1991 http://dx.doi.org/10.1017/CBO9780511840371 Zbl0729.15001
- [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 Zbl0389.65018
- [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 Zbl1058.15029
- [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 Zbl1102.15006
- [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 Zbl1051.47003
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