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

International Journal of Applied Mathematics and Computer Science (2001)

- Volume: 11, Issue: 6, page 1285-1310
- ISSN: 1641-876X

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topKarelin, Irina, and Lerer, Leonid. "Matrix quadratic equations column/row reduced factorizations and an inertia theorem for matrix polynomials." International Journal of Applied Mathematics and Computer Science 11.6 (2001): 1285-1310. <http://eudml.org/doc/207556>.

@article{Karelin2001,

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 (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 . 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.},

author = {Karelin, Irina, Lerer, Leonid},

journal = {International Journal of Applied Mathematics and Computer Science},

keywords = {column (row) reduced polynomials; extremal solutions; inertia; matrix quadratic equations; algebraic Riccati equation; factorization; Bezoutians; Bézoutians; controllability; observability},

language = {eng},

number = {6},

pages = {1285-1310},

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

url = {http://eudml.org/doc/207556},

volume = {11},

year = {2001},

}

TY - JOUR

AU - Karelin, Irina

AU - Lerer, Leonid

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

JO - International Journal of Applied Mathematics and Computer Science

PY - 2001

VL - 11

IS - 6

SP - 1285

EP - 1310

AB - 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 (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 . 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.

LA - eng

KW - column (row) reduced polynomials; extremal solutions; inertia; matrix quadratic equations; algebraic Riccati equation; factorization; Bezoutians; Bézoutians; controllability; observability

UR - http://eudml.org/doc/207556

ER -

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