Identifying Definite Quadratic Matrix Polynomials

Triangularizing Quadratic Matrix Polynomials

We show that any regular quadratic matrix polynomial can be reduced to an upper triangular quadratic matrix polynomial over the complex numbers preserving the finite and infinite elementary divisors. We characterize the real quadratic matrix polynomials that are triangularizable over the real numbers and show that those that are not triangularizable are quasi-triangularizable with diagonal bloc...

Definite Matrix Polynomials and their Linearization by Definite Pencils

Hyperbolic matrix polynomials are an important class of Hermitian matrix poly-nomials that contain overdamped quadratics as a special case. They share with definite pencils the spectral property that their eigenvalues are real and semisimple. We extend the definition of hyperbolic matrix polynomial in a way that relaxes the requirement of definiteness of the leading coefficient matrix, yielding...

Strongly Damped Quadratic Matrix Polynomials

We study the eigenvalues and eigenspaces of the quadratic matrix polynomial Mλ + sDλ + K as s → ∞, where M and K are symmetric positive definite and D is symmetric positive semi-definite. The work is motivated by its application to modal analysis of finite element models with strong linear damping. Our results yield a mathematical explanation of why too strong damping may lead to practically un...

Quadratic Matrix Inequalities and Stability of Polynomials

New relationships are enlightened between various quadratic matrix inequality conditions for stability of a scalar polynomial. It is namely shown how a recently published linear matrix inequality condition can be derived from Hermite and Lya-punov stability criteria.

Notes on Hyperbolic Matrix Polynomials and Definite Linearizations