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On connectedness of sets in the real spectra of polynomial rings

โœ Scribed by F. Lucas; J. J. Madden; D. Schaub; M. Spivakovsky


Book ID
105923765
Publisher
Springer
Year
2008
Tongue
English
Weight
520 KB
Volume
128
Category
Article
ISSN
0025-2611

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An investigation on nonconnectedness of numerical range for manic matrix polynomials L( ) is undertaking here. The distribution of eigenvalues of L(1) to the components of numerical range and some other algebraic properties are also presented.

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We investigate conditions on a square matrix M for which every LCP(M, y 1 (with q arbitrary) has a connected solution set. We show that a matrix with this property is necessarily fully semimonotone. Using degree theory, we show that the solution set of LCP(M, q) corresponding to a P,-matrix is conn