### Abstract

Motivated by the observation that there exists one-to-one correspondence between column space decompositions and row space decompositions of a matrix, the class of matrices dominated by this matrix under '≤' is characterized in terms of characteristic of column space decompositions, where ≤ is a matrix partial order such as the star partial order, the sharp partial order, and the core partial order. The dominance property of the minus partial order over the other partial orders in the discussion resulted in providing a new definition of shorted matrix of a matrix with respect to column space decomposition. Also, extensions of a few results given in [O.M. Baksalary and G. Trenkler. Core inverse of matrices. Linear Multilinear Algebra, 58:681-697, 2010.] are presented in this paper.

Original language | English |
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Pages (from-to) | 795-815 |

Number of pages | 21 |

Journal | Electronic Journal of Linear Algebra |

Volume | 26 |

Publication status | Published - 2013 |

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### All Science Journal Classification (ASJC) codes

- Algebra and Number Theory

### Cite this

*Electronic Journal of Linear Algebra*,

*26*, 795-815.

}

*Electronic Journal of Linear Algebra*, vol. 26, pp. 795-815.

**Column space decomposition and partial order on matrices.** / Eagambaram, N.; Manjunatha Prasad, K.; Mohana, K. S.

Research output: Contribution to journal › Article

TY - JOUR

T1 - Column space decomposition and partial order on matrices

AU - Eagambaram, N.

AU - Manjunatha Prasad, K.

AU - Mohana, K. S.

PY - 2013

Y1 - 2013

N2 - Motivated by the observation that there exists one-to-one correspondence between column space decompositions and row space decompositions of a matrix, the class of matrices dominated by this matrix under '≤' is characterized in terms of characteristic of column space decompositions, where ≤ is a matrix partial order such as the star partial order, the sharp partial order, and the core partial order. The dominance property of the minus partial order over the other partial orders in the discussion resulted in providing a new definition of shorted matrix of a matrix with respect to column space decomposition. Also, extensions of a few results given in [O.M. Baksalary and G. Trenkler. Core inverse of matrices. Linear Multilinear Algebra, 58:681-697, 2010.] are presented in this paper.

AB - Motivated by the observation that there exists one-to-one correspondence between column space decompositions and row space decompositions of a matrix, the class of matrices dominated by this matrix under '≤' is characterized in terms of characteristic of column space decompositions, where ≤ is a matrix partial order such as the star partial order, the sharp partial order, and the core partial order. The dominance property of the minus partial order over the other partial orders in the discussion resulted in providing a new definition of shorted matrix of a matrix with respect to column space decomposition. Also, extensions of a few results given in [O.M. Baksalary and G. Trenkler. Core inverse of matrices. Linear Multilinear Algebra, 58:681-697, 2010.] are presented in this paper.

UR - http://www.scopus.com/inward/record.url?scp=84888358267&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84888358267&partnerID=8YFLogxK

M3 - Article

VL - 26

SP - 795

EP - 815

JO - Electronic Journal of Linear Algebra

JF - Electronic Journal of Linear Algebra

SN - 1081-3810

ER -