Cell-triangular and cell-diagonal factorizations of cell-triangular and cell-diagonal polynomial matrices

Petrichkovich, V. M.

doi:10.1007/bf01157677

Cited by 10 publications

(3 citation statements)

References 3 publications

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“…Îäèí iç ìåòîäiâ ðîçâ'ÿçóâàííÿ ìàòðè÷íîãî ïîëiíîìiàëüíîãî ðiâíÿííÿ (1) ðóí-òó¹òüñÿ íà çâåäåííi öüîãî ðiâíÿííÿ äî ðiâíîñèëüíîãî ìàòðè÷íîãî ðiâíÿííÿ òàêîãî òèïó ç ìàòðèöÿìè-êîåôiöi¹íòàìè íàä ïîëåì, ïðè öüîìó çàñòîñîâóþòüñÿ ñóïðîâiäíi ìàòðèöi ìàòðè÷íèõ ïîëiíîìiâ [7], [8, ñ. 240], [9].…”

Section: Mathematics Subject Classication: 15a24 11r04unclassified

Matrix linear unilateral and bilateral equations over quadratic rings

Ladzoryshyn¹,

Petrychkovych²

2019

vmm

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Section: Mathematics Subject Classication: 15a24 11r04unclassified

Matrix linear unilateral and bilateral equations over quadratic rings

Ladzoryshyn¹,

Petrychkovych²

2019

vmm

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“…The conditions of uniqueness of solutions of bounded degree minimal solutions of matrix linear polynomial equations 1.5 were found in [16][17][18][19] . We present the conditions of uniqueness of particular solutions of matrix linear equation over a commutative Bezout domain R. 1.…”

Section: The Uniqueness Of Particular Solutions Of the Matrix Linear mentioning

confidence: 99%

The Matrix Linear Unilateral and Bilateral Equations with Two Variables over Commutative Rings

Джалюк

Petrychkovych

2012

ISRN Algebra

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“…Therefore, when we describe the solutions of such equations, it is important to establish their minimal degrees. Some estimations of the degrees of the solutions of the matrix polynomial equation (2) are known in [1,5,9]. In [1], it has been established that if in the matrix polynomial equation (2) both matrices A(λ), B(λ) are regular, then there exists a solution X(λ), Y(λ), such that degX(λ) < degB(λ), degY(λ) < degA(λ)…”

Section: Introductionmentioning

confidence: 99%

The structure of solutions of the matrix linear unilateral polynomial equation with two variables

Джалюк

Petrychkovych

2017

Carpathian Math. Publ.

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We investigate the structure of solutions of the matrix linear polynomial equation A(λ)X(λ) + B(λ)Y(λ) = C(λ), in particular, possible degrees of the solutions. The solving of this equation is reduced to the solving of the equivalent matrix polynomial equation with matrix coefficients in triangular forms with invariant factors on the main diagonals, to which the matrices A(λ), B(λ) and C(λ) are reduced by means of semiscalar equivalent transformations. On the basis of it, we have pointed out the bounds of the degrees of the matrix polynomial equation solutions. Necessary and sufficient conditions for the uniqueness of a solution with a minimal degree are established. An effective method for constructing minimal degree solutions of the equations is suggested. In this article, unlike well-known results about the estimations of the degrees of the solutions of the matrix polynomial equations in which both matrix coefficients are regular or at least one of them is regular, we have considered the case when the matrix polynomial equation has arbitrary matrix coefficients A(λ) and B(λ).

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Cell-triangular and cell-diagonal factorizations of cell-triangular and cell-diagonal polynomial matrices

Cited by 10 publications

References 3 publications

Matrix linear unilateral and bilateral equations over quadratic rings

Matrix linear unilateral and bilateral equations over quadratic rings

The Matrix Linear Unilateral and Bilateral Equations with Two Variables over Commutative Rings

The structure of solutions of the matrix linear unilateral polynomial equation with two variables

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