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1 Discussiones Mathematicae Probability and Statistics

1 2008

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Certain new M-matrices and their properties with applications

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Mohan R. , Kageyama S. , Lee M. , Yang G.

Discussiones Mathematicae Probability and Statistics

2008

tom 28

nr 2

183-207

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 M-matrices have been considered. Also we will make a mention of certain applications of these M-matrices in signal and communication processing, and network systems and end with some open problems.