Az Eszterházy Károly Tanárképző Főiskola Tudományos Közleményei. 1991. (Acta Academiae Paedagogicae Agriensis : Nova series ; Tom. 20)

Aleksander Grytczuk and Marek Szal ko ws ki: Spectral proferties of some matrices

- <13 ALEKSANDER GRYTCZUK AND MAREK SZALKOVSKI SFECTRAL PROPERTIES OF SOME MATRICES ABSTRACT: In this paper we show some spectral properties of matrices

. Among others we prove some inequalities for the characteristic roots of matrices satisfying some conditions. We also give a new proof for a theorem of SzuIc

. In 1984 N.V. Kuharenko 123 proved the following spectral property of nxn real matrix A. THEOREM A CN.W. KUHARENKO)

. Let A = (a. .) be an nxn real V ,1 matrix and let Tr A = 0 and A_ = 5 [a.

.a

..-a. .a

..1 > 0. 2 ^ liijj WJO 1 £ i < j £ r, Then there exists at least one pair of complex-conjugate eigen—values = ck * i

dk of A such that * + I A, • k k n 2 This theorem has application in the theory of dynamical systems. In 1988 T.Szulc 131 gave the following generalization of Theorem A. THEOREM B. Let A = Ca. .) be nxn real matrix such that «- J Tr

2 A < -^t- A„ n—

1 2