Certain new M-matrices and their properties with applications

Ratnakaram N. Mohan; Sanpei Kageyama; Moon H. Lee; G. Yang

Discussiones Mathematicae Probability and Statistics (2008)

  • Volume: 28, Issue: 2, page 183-207
  • ISSN: 1509-9423

Abstract

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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.

How to cite

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Ratnakaram N. Mohan, et al. "Certain new M-matrices and their properties with applications." Discussiones Mathematicae Probability and Statistics 28.2 (2008): 183-207. <http://eudml.org/doc/277044>.

@article{RatnakaramN2008,
abstract = {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.},
author = {Ratnakaram N. Mohan, Sanpei Kageyama, Moon H. Lee, G. Yang},
journal = {Discussiones Mathematicae Probability and Statistics},
keywords = {M-matrices; non-orthogonality; orthogonal number; Hadamard matrix; partially balanced incomplete block (PBIB) design; regular graph},
language = {eng},
number = {2},
pages = {183-207},
title = {Certain new M-matrices and their properties with applications},
url = {http://eudml.org/doc/277044},
volume = {28},
year = {2008},
}

TY - JOUR
AU - Ratnakaram N. Mohan
AU - Sanpei Kageyama
AU - Moon H. Lee
AU - G. Yang
TI - Certain new M-matrices and their properties with applications
JO - Discussiones Mathematicae Probability and Statistics
PY - 2008
VL - 28
IS - 2
SP - 183
EP - 207
AB - 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.
LA - eng
KW - M-matrices; non-orthogonality; orthogonal number; Hadamard matrix; partially balanced incomplete block (PBIB) design; regular graph
UR - http://eudml.org/doc/277044
ER -

References

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