ON EIGENVALUES OF QUADRATIC MATRIX POLYNOMIALS AND THEIR PERTURBATIONS

Following the terminology used by Gohberg, Lancaster, and Rodman, the main results of the paper are as follows. (i) Studying the values of t he partial multiplicities of a matrix polynomial A(lambda) = lambda(2) I + lambda C + K with hermitian coefficients at real eigenvalues lambd a(0) and determining sharp bounds for the highest degree d of the fact or (lambda - lambda(0))(d) in the bivariate polynomial t(lambda, epsil on) = det(A(lambda)+ lambda epsilon C). (ii) Finding conditions on gen eral matrices C and K implying that the leading exponent in the Puiseu x expansion of the zero lambda(epsilon) Of t(lambda, epsilon) = 0 near lambda(0) is 1/a, where a is the algebraic multiplicity of lambda(0).