Displaying similar documents to “On the basic contrasts in PBIB designs”

Two-level Cretan matrices constructed using SBIBD

N. A. Balonin, Jennifer Seberry (2015)

Special Matrices

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Two-level Cretan matrices are orthogonal matrices with two elements, x and y. At least one element per row and column is 1 and the other element has modulus ≤ 1. These have been studied in the Russian literature for applications in image processing and compression. Cretan matrices have been found by both mathematical and computational methods but this paper concentrates on mathematical solutions for the first time. We give, for the first time, families of Cretan matrices constructed...

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...

Certain new M-matrices and their properties with applications

Ratnakaram N. Mohan, Sanpei Kageyama, Moon H. Lee, G. Yang (2008)

Discussiones Mathematicae Probability and Statistics

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The Mₙ-matrix was defined by Mohan [21] who has shown a method of constructing (1,-1)-matrices and studied some of their properties. The (1,-1)-matrices were constructed and studied by Cohn [6], Ehrlich [9], Ehrlich and Zeller [10], and Wang [34]. But in this paper, while giving some resemblances of this matrix with a Hadamard matrix, and by naming it as an M-matrix, we show how to construct partially balanced incomplete block designs and some regular graphs by it. Two types of these...

Complex Hadamard Matrices contained in a Bose–Mesner algebra

Takuya Ikuta, Akihiro Munemasa (2015)

Special Matrices

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Acomplex Hadamard matrix is a square matrix H with complex entries of absolute value 1 satisfying HH* = nI, where * stands for the Hermitian transpose and I is the identity matrix of order n. In this paper, we first determine the image of a certain rational map from the d-dimensional complex projective space to Cd(d+1)/2. Applying this result with d = 3, we give constructions of complex Hadamard matrices, and more generally, type-II matrices, in the Bose–Mesner algebra of a certain 3-class...

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...

Characterization of α1 and α2-matrices

Rafael Bru, Ljiljana Cvetković, Vladimir Kostić, Francisco Pedroche (2010)

Open Mathematics

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This paper deals with some properties of α1-matrices and α2-matrices which are subclasses of nonsingular H-matrices. In particular, new characterizations of these two subclasses are given, and then used for proving algebraic properties related to subdirect sums and Hadamard products.