### Abstract

Goller (1986) gave an explicit expression for a shorted matrix as defined by Mitra and Puri (1982) and Mitra (1982) in situations where the shorted matrix is not unique. In this paper, the authors provide an alternative approach to the same problem which may give deeper insight into it. In this development, certain concepts such as quasiidempotent matrices and the separability of subspaces of row and column spans of a matrix with reference to the same matrix play an interesting role, as shown by Mitra. Under certain regularity conditions the shorted matrix has some interesting properties similar to the ones noted by Anderson and Trapp for their unique shorted operator. A detailed investigation is made of how many of these properties are realized in the nonunique case.

Original language | English |
---|---|

Pages (from-to) | 41-70 |

Number of pages | 30 |

Journal | Linear Algebra and Its Applications |

Volume | 237-238 |

DOIs | |

Publication status | Published - 04-1996 |

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### All Science Journal Classification (ASJC) codes

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

### Cite this

*Linear Algebra and Its Applications*,

*237-238*, 41-70. https://doi.org/10.1016/0024-3795(95)00599-4

}

*Linear Algebra and Its Applications*, vol. 237-238, pp. 41-70. https://doi.org/10.1016/0024-3795(95)00599-4

**The nonunique shorted matrix.** / Mitra, Sujit Kumar; Prasad, K. Manjunatha.

Research output: Contribution to journal › Article

TY - JOUR

T1 - The nonunique shorted matrix

AU - Mitra, Sujit Kumar

AU - Prasad, K. Manjunatha

PY - 1996/4

Y1 - 1996/4

N2 - Goller (1986) gave an explicit expression for a shorted matrix as defined by Mitra and Puri (1982) and Mitra (1982) in situations where the shorted matrix is not unique. In this paper, the authors provide an alternative approach to the same problem which may give deeper insight into it. In this development, certain concepts such as quasiidempotent matrices and the separability of subspaces of row and column spans of a matrix with reference to the same matrix play an interesting role, as shown by Mitra. Under certain regularity conditions the shorted matrix has some interesting properties similar to the ones noted by Anderson and Trapp for their unique shorted operator. A detailed investigation is made of how many of these properties are realized in the nonunique case.

AB - Goller (1986) gave an explicit expression for a shorted matrix as defined by Mitra and Puri (1982) and Mitra (1982) in situations where the shorted matrix is not unique. In this paper, the authors provide an alternative approach to the same problem which may give deeper insight into it. In this development, certain concepts such as quasiidempotent matrices and the separability of subspaces of row and column spans of a matrix with reference to the same matrix play an interesting role, as shown by Mitra. Under certain regularity conditions the shorted matrix has some interesting properties similar to the ones noted by Anderson and Trapp for their unique shorted operator. A detailed investigation is made of how many of these properties are realized in the nonunique case.

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UR - http://www.scopus.com/inward/citedby.url?scp=0040889453&partnerID=8YFLogxK

U2 - 10.1016/0024-3795(95)00599-4

DO - 10.1016/0024-3795(95)00599-4

M3 - Article

VL - 237-238

SP - 41

EP - 70

JO - Linear Algebra and Its Applications

JF - Linear Algebra and Its Applications

SN - 0024-3795

ER -