Creator:

Karelin, Irina ; Lerer, Leonid

Contributor:

Curtain, Ruth - ed. ; Kaashoek, Rien - ed.

Title:

Matrix quadratic equations, column/row reduced factorizations and an inertia theorem for matrix polynomials

Subtitle:

Infinite-Dimensional Systems Theory and Operator Theory

Group publication title:

AMCS, volume 11 (2001)

Subject and Keywords:

matrix quadratic equations ; Bezoutians ; inertia ; column (row) reduced polynomials ; factorization ; algebraic Riccati equation ; extremal solutions

Abstract:

It is shown that a certain Bezout operator provides a bijective correspondence between the solutions of the matrix quadratic equation and factorizatons of a certain matrix polynomial G([lambda]) (which is a specification of a Popov-type function) into a product of row and column reduced polynomials. Special attention is paid to the symmetric case, i.e. to the Algebraic Riccati Equation. ; In particular, it is shown that extremal solutions of such equations correspond to spectral factorizations of G([lambda]). The proof of these results depends heavily on a new inertia theorem for matrix polynomials which is also one of the main results in this paper.

Publisher:

Zielona Góra: Uniwersytet Zielonogórski

Date:

2001

Resource Type:

artykuł

Pages:

1285-1310

Source:

AMCS, volume 11, number 6 (2001) ; click here to follow the link

Language:

eng

License CC BY 4.0:

click here to follow the link

Rights:

Biblioteka Uniwersytetu Zielonogórskiego