Geodesic
Certain new M-matrices and their properties with applications
Discussiones Mathematicae. Probability and Statistics, Tome 28 (2008) no. 2, pp. 183-207

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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 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.
Keywords: M-matrices, non-orthogonality, orthogonal number, Hadamard matrix, partially balanced incomplete block (PBIB) design, regular graph 
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Mohan, Ratnakaram; Kageyama, Sanpei; Lee, Moon; Yang, G. Certain new M-matrices and their properties with applications. Discussiones Mathematicae. Probability and Statistics, Tome 28 (2008) no. 2, pp. 183-207. http://geodesic.mathdoc.fr/item/DMPS_2008_28_2_a1/