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A new characterization of generalized complementary basic matrices

100%
Fiedler M., Hall F. J.
Special Matrices
|
2014
|
tom 2
|
nr 1
EN
In this paper, a new characterization of previously studied generalized complementary basic matrices is obtained. It is in terms of ranks and structure ranks of submatrices defined by certain diagonal positions. The results concern both the irreducible and general cases.
2
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A New Characterization of Generalized Complementary Basic Matrices

100%
Fiedler M., Hall F. J.
Special Matrices
|
2014
|
tom 2
|
nr 1
EN
In this paper, a new characterization of previously studied generalized complementary basic matrices is obtained. It is in terms of ranks and structure ranks of submatrices defined by certain diagonal positions. The results concern both the irreducible and general cases
3
Content available remote

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.
4
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Sign patterns of J-orthogonal matrices

81%
Hall F. J., Li Z., Parnass C. T., Rozložník M.
Special Matrices
|
2017
|
tom 5
|
nr 1
225-241
EN
This paper builds upon the results in the article “G-matrices, J-orthogonal matrices, and their sign patterns", Czechoslovak Math. J. 66 (2016), 653-670, by Hall and Rozloznik. A number of further general results on the sign patterns of the J-orthogonal matrices are proved. Properties of block diagonal matrices and their sign patterns are examined. It is shown that all 4 × 4 full sign patterns allow J-orthogonality. Important tools in this analysis are Theorem 2.2 on the exchange operator and Theorem 3.2 on the characterization of J-orthogonal matrices in the paper “J-orthogonal matrices: properties and generation", SIAM Review 45 (3) (2003), 504-519, by Higham. As a result, it follows that for n ≤4 all n×n full sign patterns allow a J-orthogonal matrix as well as a G-matrix. In addition, the 3 × 3 sign patterns of the J-orthogonal matrices which have zero entries are characterized.
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