Outer inverses and Jacobi type identities

Ravindra B. Bapat; Manjunatha Prasad Karantha; Nupur Nandini; Divya P. Shenoy

doi:10.1016/j.laa.2017.09.025

Outer inverses and Jacobi type identities

Ravindra B. Bapat, Manjunatha Prasad Karantha, Nupur Nandini, Divya P. Shenoy

Research output: Contribution to journal › Article › peer-review

1 Citation (Scopus)

Abstract

We consider matrices over a commutative ring and characterize the class of outer inverses for which Jacobi type identities can be extended. We obtain a necessary and sufficient condition for the existence of Rao-regular Drazin inverse in terms of sum of principal minors of A^k for some k. Also, we obtain determinantal formula for the Rao-regular Drazin inverse. Conjectures are formulated which give expressions for outer inverse and the conjectures are proved in some special cases.

Original language	English
Pages (from-to)	274-294
Number of pages	21
Journal	Linear Algebra and Its Applications
Volume	536
DOIs	https://doi.org/10.1016/j.laa.2017.09.025
Publication status	Published - 01-01-2018

All Science Journal Classification (ASJC) codes

Algebra and Number Theory
Numerical Analysis
Geometry and Topology
Discrete Mathematics and Combinatorics

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10.1016/j.laa.2017.09.025

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abstract = "We consider matrices over a commutative ring and characterize the class of outer inverses for which Jacobi type identities can be extended. We obtain a necessary and sufficient condition for the existence of Rao-regular Drazin inverse in terms of sum of principal minors of Ak for some k. Also, we obtain determinantal formula for the Rao-regular Drazin inverse. Conjectures are formulated which give expressions for outer inverse and the conjectures are proved in some special cases.",

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T1 - Outer inverses and Jacobi type identities

AU - Bapat, Ravindra B.

AU - Karantha, Manjunatha Prasad

AU - Nandini, Nupur

AU - Shenoy, Divya P.

PY - 2018/1/1

Y1 - 2018/1/1

N2 - We consider matrices over a commutative ring and characterize the class of outer inverses for which Jacobi type identities can be extended. We obtain a necessary and sufficient condition for the existence of Rao-regular Drazin inverse in terms of sum of principal minors of Ak for some k. Also, we obtain determinantal formula for the Rao-regular Drazin inverse. Conjectures are formulated which give expressions for outer inverse and the conjectures are proved in some special cases.

AB - We consider matrices over a commutative ring and characterize the class of outer inverses for which Jacobi type identities can be extended. We obtain a necessary and sufficient condition for the existence of Rao-regular Drazin inverse in terms of sum of principal minors of Ak for some k. Also, we obtain determinantal formula for the Rao-regular Drazin inverse. Conjectures are formulated which give expressions for outer inverse and the conjectures are proved in some special cases.

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U2 - 10.1016/j.laa.2017.09.025

DO - 10.1016/j.laa.2017.09.025

M3 - Article

AN - SCOPUS:85030249016

SN - 0024-3795

VL - 536

SP - 274

EP - 294

JO - Linear Algebra and Its Applications

JF - Linear Algebra and Its Applications

ER -

Outer inverses and Jacobi type identities

Abstract

All Science Journal Classification (ASJC) codes

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