Displaying similar documents to “Common Transversals Of Finite Families”

Elementary triangular matrices and inverses of k-Hessenberg and triangular matrices

Luis Verde-Star (2015)

Special Matrices

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We use elementary triangular matrices to obtain some factorization, multiplication, and inversion properties of triangular matrices. We also obtain explicit expressions for the inverses of strict k-Hessenberg matrices and banded matrices. Our results can be extended to the cases of block triangular and block Hessenberg matrices. An n × n lower triangular matrix is called elementary if it is of the form I + C, where I is the identity matrix and C is lower triangular and has all of its...

Pentadiagonal Companion Matrices

Brydon Eastman, Kevin N. Vander Meulen (2016)

Special Matrices

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The class of sparse companion matrices was recently characterized in terms of unit Hessenberg matrices. We determine which sparse companion matrices have the lowest bandwidth, that is, we characterize which sparse companion matrices are permutationally similar to a pentadiagonal matrix and describe how to find the permutation involved. In the process, we determine which of the Fiedler companion matrices are permutationally similar to a pentadiagonal matrix. We also describe how to find...

An Inferentially Many-Valued Two-Dimensional Notion of Entailment

Carolina Blasio, João Marcos, Heinrich Wansing (2017)

Bulletin of the Section of Logic

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Starting from the notions of q-entailment and p-entailment, a two-dimensional notion of entailment is developed with respect to certain generalized q-matrices referred to as B-matrices. After showing that every purely monotonic singleconclusion consequence relation is characterized by a class of B-matrices with respect to q-entailment as well as with respect to p-entailment, it is observed that, as a result, every such consequence relation has an inferentially four-valued characterization....

Modifying the tropical version of Stickel's key exchange protocol

Any Muanalifah, Sergei Sergeev (2020)

Applications of Mathematics

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A tropical version of Stickel's key exchange protocol was suggested by Grigoriev and Shpilrain (2014) and successfully attacked by Kotov and Ushakov (2018). We suggest some modifications of this scheme that use commuting matrices in tropical algebra and discuss some possibilities of attacks on these new modifications. We suggest some simple heuristic attacks on one of our new protocols, and then we generalize the Kotov and Ushakov attack on tropical Stickel's protocol and discuss the...

A Hadamard product involving inverse-positive matrices

Gassó Maria T., Torregrosa Juan R., Abad Manuel (2015)

Special Matrices

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In this paperwe study the Hadamard product of inverse-positive matrices.We observe that this class of matrices is not closed under the Hadamard product, but we show that for a particular sign pattern of the inverse-positive matrices A and B, the Hadamard product A ◦ B−1 is again an inverse-positive matrix.