Minus partial order and rank 1 summands

Bhat, Nayan K and Karantha, Manjunatha Prasad (2018) Minus partial order and rank 1 summands. Bulletin of Kerala Mathematics Association, 16 (1). pp. 47-58. ISSN 0973-2721

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Abstract

In this paper 'rank 1 summand' of a matrix is defined and some interesting properties of rank 1 summands are studied. It has been proved that two matrices are related by minus partial order if and only if the sets of rank 1 summands of corresponding matrices are related by set inclusion partial order. Motivated from the study of rank 1 summands, the concept of bi-orthogonalization proess is developed imitating Gram-Schmidt process. This process provides a new approach to study the shorted matrices. We also observe that a shorted matrix can be obtained easily from a maximal bi-orthonormal set which is obtained in bi-orthogonalization process.

Item Type: Article
Uncontrolled Keywords: Generalized inverse; minus partial order; shorted matrix; rank 1 summand.
Subjects: Departments at MU > Statistics
Depositing User: KMC Library
Date Deposited: 10 Aug 2018 09:25
Last Modified: 10 Aug 2018 09:25
URI: http://eprints.manipal.edu/id/eprint/151744

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