Document Type: Research Paper
Authors
- Zahra Boor Boor Azimi ^{1}
- Gholamreza Aghamollaei ^{} ^{2}
^{1} Department of Mathematics, Kerman Branch, Islamic Azad University, Kerman, Iran.
^{2} Department of Pure Mathematics, Faculty of Mathematics and Computer, Shahid Bahonar University of Kerman, Kerman, Iran.
Abstract
In this paper, the notions of pseudofield of values and joint pseudofield of values of matrix polynomials are introduced and some of their algebraic and geometrical properties are studied. Moreover, the relationship between the pseudofield of values of a matrix polynomial and the pseudofield of values of its companion linearization is stated, and then some properties of the augmented field of values of basic A-factor block circulant matrices are investigated.
Keywords
[1] Gh. Aghamollaei and A. Salemi, Polynomial numerical hulls of matrix polynomials, II, Linear Multilinear Algebra, 59 (2011), pp. 291-302.
[2] J.C.R. Claeyssen and L.A.S. Leal, Diagonalization and spectral decomposition of factor block circulant matrices, Linear Algebra Appl., 99 (1988), pp. 41-61.
[3] M. Eiermann, Field of values and iterative methods, Linear Algebra Appl., 180 (1993), pp. 167-197.
[4] I. Gohberg, P. Lancaster and L. Rodman, Matrix Polynomials, Academic Press, New York, 1982.
[5] K.E. Gustafson and D.K.M. Rao, Numerical Range: The Field of values of Linear Operators and Matrices, Springer-Verlage, New York, 1997.
[6] R.A. Horn and Ch. Johnson, Topics in Matrix Analysis, Cambridge University Press, Cambridge, 1991.
[7] M. Khakshour, Gh. Aghamollaei, and A. Sheikhhosseini, Field of values of perturbed matrices and quantum states, Turkish J. Math., 42 (2018), pp. 647-655.
[8] C.K. Li and L. Rodman, Numerical range of matrix polynomials, SIAM J. Matrix Anal. Appl., 15 (1994), pp. 1256-1265.
[9] F. Tisseur and N.J. Higham, Structured pseudospectra for polynomial eigenvalue problems with applications, SIAM J. Matrix Anal. Appl., 23 (2001), pp. 187-208.
[10] L.N. Trefethen and M. Embree, Spectra and Pseudospectra, The Bihavior of Nonnormal Matrices and Operators, Princeton University Press, Princeton, 2005.