# 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

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- [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
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