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Combinatorial aspects of generalized complementary basic matrices

100%
Fiedler M., Hall F.
Open Mathematics
|
2013
|
tom 11
|
nr 12
2186-2196
EN
This paper extends some properties of the generalized complementary basic matrices, in particular, in a combinatorial direction. These include inheritance (such as for Alternating Sign Matrices), spectral, and sign pattern matrix (including sign nonsingularity) properties.
2
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Factorizable matrices

100%
Fiedler M., Hall F. J.
Special Matrices
|
2013
|
tom 1
3-9
EN
We study square matrices which are products of simpler factors with the property that any ordering of the factors yields a matrix cospectral with the given matrix. The results generalize those obtained previously by the authors.
3
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An approach based on matrix polynomials for linear systems of partial differential equations

84%
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.
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