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Artykuł dostępny w postaci pełnego tekstu - kliknij by otworzyć plik
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Zero-term rank preservers of integer matrices

100%
Song S.-Z., Jun Y.-B.
Discussiones Mathematicae - General Algebra and Applications
|
2006
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tom 26
|
nr 2
155-161
EN
The zero-term rank of a matrix is the minimum number of lines (row or columns) needed to cover all the zero entries of the given matrix. We characterize the linear operators that preserve the zero-term rank of the m × n integer matrices. That is, a linear operator T preserves the zero-term rank if and only if it has the form T(A)=P(A ∘ B)Q, where P, Q are permutation matrices and A ∘ B is the Schur product with B whose entries are all nonzero integers.
2
Content available remote

A Simple Proof of the Polar Decomposition Theorem

100%
Wójcik P.
Annales Mathematicae Silesianae
|
2017
|
tom 31
|
nr 1
165-171
EN
In this expository paper, we present a new and easier proof of the Polar Decomposition Theorem. Unlike in classical proofs, we do not use the square root of a positive matrix. The presented proof is accessible to a broad audience.
3
Content available remote

An approach based on matrix polynomials for linear systems of partial differential equations

88%
Shayanfar N., Hadizadeh M.
Special Matrices
|
2013
|
tom 1
42-48
EN
In this paper, an approach based on matrix polynomials is introduced for solving linear systems of partial differential equations. The main feature of the proposed method is the computation of the Smith canonical form of the assigned matrix polynomial to the linear system of PDEs, which leads to a reduced system. It will be shown that the reduced one is an independent system of PDEs having only one unknown in each equation. A comparison of the results for several test problems reveals that the method is very effective and convenient. The basic idea described in this paper can be employed to solve other linear functional systems.
4
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On differential sandwich theorems of analytic functions defined by certain linear operator

88%
Aouf M. K., Seoudy T. M.
Annales Universitatis Mariae Curie-Skłodowska, sectio A – Mathematica
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2010
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tom 64
|
nr 2
EN
In this paper, we obtain some applications of first order differential subordination and superordination results involving certain linear operator and other linear operators for certain normalized analytic functions. Some of our results improve and generalize previously known results.
5
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Subexponential Solutions of Linear Volterra Difference Equations

88%
Bohner M., Sultana N.
Nonautonomous Dynamical Systems
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2015
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tom 2
|
nr 1
EN
We study the asymptotic behavior of the solutions of a scalar convolution sum-difference equation. The rate of convergence of the solution is found by determining the asymptotic behavior of the solution of the transient renewal equation.
6
Artykuł dostępny w postaci pełnego tekstu - kliknij by otworzyć plik
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Rank and perimeter preserver of rank-1 matrices over max algebra

63%
Song S.-Z., Kang K.-T.
Discussiones Mathematicae - General Algebra and Applications
|
2003
|
tom 23
|
nr 2
125-137
EN
For a rank-1 matrix $A = a ⊗ b^{t}$ over max algebra, we define the perimeter of A as the number of nonzero entries in both a and b. We characterize the linear operators which preserve the rank and perimeter of rank-1 matrices over max algebra. That is, a linear operator T preserves the rank and perimeter of rank-1 matrices if and only if it has the form T(A) = U ⊗ A ⊗ V, or $T(A) = U ⊗ A^{t} ⊗ V$ with some monomial matrices U and V.
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