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Skew Spectrum of the Cartesian Product of an Oriented Graph with an Oriented Hypercube Read chapter Read first chapter

2013 | OriginalPaper | Chapter

The Reverse Order Law in Indefinite Inner Product Spaces

Author : Sachindranath Jayaraman

Published in: Combinatorial Matrix Theory and Generalized Inverses of Matrices

Publisher: Springer India

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Abstract

The aim of this short note is to present a few reverse order laws for the Moore–Penrose inverse and the group inverse (when it exists) in indefinite inner product spaces, with respect to the indefinite matrix product. We also point out its relationship with the star and sharp orders, respectively.

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previous chapter Moore–Penrose Inverse of Perturbed Operators on Hilbert Spaces
next chapter Generalized Inverses and Approximation Numbers
Literature
1.
Baksalary, J.K., Baksalary, O.M.: An invariance property related to the reverse order law. Linear Algebra Appl. 410, 64–69 (2005) MathSciNetMATHCrossRef
2.
Benitez, J., Liu, X., Zhong, J.: Some results on matrix partial orderings and reverse order law. Electron. J. Linear Algebra 20, 254–273 (2010) MathSciNetMATH
3.
Blackwood, B., Jain, S.K., Prasad, K.M., Srivastava, A.K.: Shorted operators relative to a partial order in a regular ring. Commun. Algebra 37(11), 4141–4152 (2009) MathSciNetMATHCrossRef
4.
Jayaraman, S.: EP matrices in indefinite inner product spaces. Funct. Anal. Approx. Comput. 4(2), 23–31 (2012)
5.
Jayaraman, S.: Nonnegative generalized inverses in indefinite inner product spaces. Filomat, accepted for publication
6.
Mitra, S.K., Bhimasankaram, P., Malik, S.B.: Matrix Partial Orders, Shorted Operators and Applications. Series in Algebra, vol. 10. World Scientific, Singapore (2010) MATH
7.
Mosic, D., Djordjevic, D.S.: Reverse order law for the Moore–Penrose inverse in C∗ algebras. Electron. J. Linear Algebra 22, 92–111 (2011) MathSciNetMATH
8.
Mosic, D., Djordjevic, D.S.: Further results on the reverse order law for the Moore–Penrose inverse in rings with involution. Appl. Math. Comput. 218(4), 1476–1483 (2011) MathSciNetCrossRef
9.
Ramanathan, K., Sivakumar, K.C.: Theorems of the alternative in indefinite inner product spaces. J. Optim. Theory Appl. 137(1), 99–104 (2008) MathSciNetMATHCrossRef
10.
Ramanathan, K., Sivakumar, K.C.: Nonnegative Moore–Penrose inverse of a Gram matrix in an indefinite inner product space. J. Optim. Theory Appl. 140(1), 189–196 (2009) MathSciNetMATHCrossRef
11.
Ramanathan, K., Kamaraj, K., Sivakumar, K.C.: Indefinite product of matrices and applications to indefinite inner product spaces. J. Anal. 12, 135–142 (2004) MathSciNetMATH
12.
Malik, S.B.: Matrix partial orders and reversal law. Indian J. Pure Appl. Math. 38(6), 569–577 (2007) MathSciNetMATH
13.
Metadata
Title
The Reverse Order Law in Indefinite Inner Product Spaces
Author
Sachindranath Jayaraman
Copyright Year
2013
Publisher
Springer India
Book
Combinatorial Matrix Theory and Generalized Inverses of Matrices

Print ISBN: 978-81-322-1052-8

Electronic ISBN: 978-81-322-1053-5

Copyright Year: 2013

DOI
https://doi.org/10.1007/978-81-322-1053-5_11

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