2019
Том 71
№ 2

All Issues

Prokip V. M.

Articles: 10
Brief Communications (Ukrainian)

On the Solvability of a System of Linear Equations Over the Domain Of Principal Ideals

Prokip V. M.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 2014. - 66, № 4. - pp. 566–570

We propose new necessary and sufficient conditions for the solvability of a system of linear equations over the domain of principal ideals and an algorithm for the solution of this system.

Brief Communications (Ukrainian)

Diagonalizability of matrices over a principal ideal domain

Prokip V. M.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 2012. - 64, № 2. - pp. 283-288

A square matrix is said to be diagonalizable if it is similar to a diagonal matrix. We establish necessary and sufficient conditions for the diagonalizability of matrices over a principal ideal domain.

Brief Communications (Ukrainian)

Canonical form with respect to semiscalar equivalence for a matrix pencil with nonsingular first matrix

Prokip V. M.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 2011. - 63, № 8. - pp. 1147-1152

Polynomial matrices $A(x)$ and $B(x)$ of size $n \times n$ over a field $\mathbb{F}$ are called semiscalar equivalent if there exist a nonsingular $n \times n$ matrix $P$ over $\mathbb{F}$ and an invertible $n \times n$ matrix $Q(x)$ over $\mathbb{F}[x]$ such that $A(x) = PB(x)Q(x)$. We give a canonical form with respect to the semiscalar equivalence for a matrix pencil $A(x) = A_0x - A_1$, where $A_0$ and $A_1$ are $n \times n$ matrices over $\mathbb{F}$, and $A_0$ is nonsingular.

Article (Ukrainian)

On One Class of Divisors of Polynomial Matrices over Integral Domains

Prokip V. M.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 2003. - 55, № 8. - pp. 1099-1106

We establish conditions for the existence of a unital divisor for a polynomial matrix over an integral domain of characteristic zero in the case where its eigenvalues are known.

Brief Communications (Ukrainian)

Structure of Matrices and Their Divisors over the Domain of Principal Ideals

Prokip V. M.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 2002. - 54, № 8. - pp. 1143-1148

We investigate the structure of matrices and their divisors over the domain of principal ideals.

Brief Communications (Ukrainian)

On Multiplicativity of Canonical Diagonal Forms of Matrices over the Domain of Principal Ideals. II

Prokip V. M.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 2001. - 53, № 2. - pp. 274-277

We investigate the structure of matrices over the domain of principal ideals that possess the property of multiplicativity of canonical diagonal forms.

Brief Communications (Ukrainian)

Polynomial matrices over a factorial domain and their factorization with given characteristic polynomials

Prokip V. M.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 1998. - 50, № 10. - pp. 1438–1440

We establish conditions for the existence of a unital divisor with given characteristic polynomial of a polynomial matrix over a factorial domain.

Article (Ukrainian)

A method for finding a common linear divisor of the matrix polynomials over an arbitrary field

Khudyi M. I., Prokip V. M.

Full text (.pdf)

Ukr. Mat. Zh. - 1993. - 45, № 8. - pp. 1181–1183

Article (Ukrainian)

On the uniqueness of the unital divisor of a matrix polynomial over an arbitrary field

Prokip V. M.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 1993. - 45, № 6. - pp. 803–808

Conditions are established under which the unital divisor extracted from a matrix polynomial over an arbitrary field is determined uniquely by its characteristic polynomial. The result obtained is applied to the problem of solving matrix polynomial equations.

Article (Ukrainian)

Factorization of polynomial matrices over arbitrary fields

Petrichkovich V. M., Prokip V. M.

Full text (.pdf)

Ukr. Mat. Zh. - 1986. - 38, № 4. - pp. 478–483