Inverse complements of a matrix and applications

Author:

Nayan Bhat K.1,Karantha Manjunatha Prasad12,Eagambaram N.3

Affiliation:

1. Department of Data Science, PSPH, Manipal Academy of Higher Education, Manipal 576 104, India

2. Center for Advanced Research in Applied Mathematics and Statistics, Manipal Academy of Higher Education, Manipal 576 104, India

3. Indian Statistical Service (Retired), 12A Dr. Ambedkar Salai, Rajarajeswari Nagar, Madipakkam, Chennai 600 091, India

Abstract

In this paper, the concept of “Inverse Complemented Matrix Method”, introduced by Eagambaram (2018), has been reestablished with the help of minus partial order and several new properties of complementary matrices and the inverse of complemented matrix are discovered. Class of generalized inverses and outer inverses of given matrix are characterized by identifying appropriate inverse complement. Further, in continuation, we provide a condition equivalent to the regularity condition for a matrix to have unique shorted matrix in terms of inverse complemented matrix. Also, an expression for shorted matrix in terms of inverse complemented matrix is given.

Publisher

World Scientific Pub Co Pte Lt

Subject

Applied Mathematics,Algebra and Number Theory

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