Certain new M-matrices and their properties and applications

The Mn-matrix was defined by Mohan [20] in which he 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 [5],Wang [33], Ehrlich [8] and Ehrlich and Zeller[9]. But in this paper, while giving some resemblances of this matrix with Hadamard matrix, and by naming it as M-matrix, we show how to construct partially balanced incomplete block (PBIB) designs and some regular bipartite graphs by it. We have considered two types of these M- matrices. 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.