### Abstract

This paper is a sequel to earlier study of the authors' on the nonunique shorted matrix under the failure of regularity conditions. When A and B are real symmetric nonnegative definite (n.n.d.) matrices of the same order, Anderson and Trapp present an alternative definition of the parallel sum of Anderson and Duffin which uses a shorted version of the matrix Formula Represented Here, Λ being real symmetric n.n.d., the regularity conditions are trivially true. In the more general case, however, a similar approach based on the nonunique shorted matrix leads to a nonunique parallel sum. The extent to which the nonunique parallel sum retains the properties of parallel sum of Anderson and Duffin is examined. An interesting statistical interpretation of the parallel sum operation is provided in an appendix.

Original language | English |
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Pages (from-to) | 77-99 |

Number of pages | 23 |

Journal | Linear Algebra and Its Applications |

Volume | 259 |

Issue number | 1-3 |

Publication status | Published - 01-07-1997 |

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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*,

*259*(1-3), 77-99.

}

*Linear Algebra and Its Applications*, vol. 259, no. 1-3, pp. 77-99.

**The nonunique parallel sum.** / Mitra, Sujit Kumar; Manjunatha Prasad, K.

Research output: Contribution to journal › Article

TY - JOUR

T1 - The nonunique parallel sum

AU - Mitra, Sujit Kumar

AU - Manjunatha Prasad, K.

PY - 1997/7/1

Y1 - 1997/7/1

N2 - This paper is a sequel to earlier study of the authors' on the nonunique shorted matrix under the failure of regularity conditions. When A and B are real symmetric nonnegative definite (n.n.d.) matrices of the same order, Anderson and Trapp present an alternative definition of the parallel sum of Anderson and Duffin which uses a shorted version of the matrix Formula Represented Here, Λ being real symmetric n.n.d., the regularity conditions are trivially true. In the more general case, however, a similar approach based on the nonunique shorted matrix leads to a nonunique parallel sum. The extent to which the nonunique parallel sum retains the properties of parallel sum of Anderson and Duffin is examined. An interesting statistical interpretation of the parallel sum operation is provided in an appendix.

AB - This paper is a sequel to earlier study of the authors' on the nonunique shorted matrix under the failure of regularity conditions. When A and B are real symmetric nonnegative definite (n.n.d.) matrices of the same order, Anderson and Trapp present an alternative definition of the parallel sum of Anderson and Duffin which uses a shorted version of the matrix Formula Represented Here, Λ being real symmetric n.n.d., the regularity conditions are trivially true. In the more general case, however, a similar approach based on the nonunique shorted matrix leads to a nonunique parallel sum. The extent to which the nonunique parallel sum retains the properties of parallel sum of Anderson and Duffin is examined. An interesting statistical interpretation of the parallel sum operation is provided in an appendix.

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UR - http://www.scopus.com/inward/citedby.url?scp=0039375256&partnerID=8YFLogxK

M3 - Article

VL - 259

SP - 77

EP - 99

JO - Linear Algebra and Its Applications

JF - Linear Algebra and Its Applications

SN - 0024-3795

IS - 1-3

ER -