### Abstract

Original language | English |
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Place of Publication | København |
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Publisher | Department of Mathematics, Technical University of Denmark |

Edition | 1 |

Publication status | Published - 2004 |

Series | MAT-Report |
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Number | 2004-15 |

### Cite this

*On free matrices*. (1 ed.) København: Department of Mathematics, Technical University of Denmark. MAT-Report, No. 2004-15

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*On free matrices*. MAT-Report, no. 2004-15, 1 edn, Department of Mathematics, Technical University of Denmark, København.

**On free matrices.** / Britz, Thomas.

Research output: Book/Report › Report › Research

TY - RPRT

T1 - On free matrices

AU - Britz, Thomas

PY - 2004

Y1 - 2004

N2 - Bipartite graphs and digraphs are used to describe algebraic operations on a free matrix, including Moore-Penrose inversion, finding Schur complements, and normalized LU factorization. A description of the structural properties of a free matrix and its Moore-Penrose inverse is proved, and necessary and sufficient conditions are given for the Moore-Penrose inverse of a free matrix to be free. Several of these results are generalized with respect to a family of matrices that contains both the free matrices and the nearly reducible matrices.

AB - Bipartite graphs and digraphs are used to describe algebraic operations on a free matrix, including Moore-Penrose inversion, finding Schur complements, and normalized LU factorization. A description of the structural properties of a free matrix and its Moore-Penrose inverse is proved, and necessary and sufficient conditions are given for the Moore-Penrose inverse of a free matrix to be free. Several of these results are generalized with respect to a family of matrices that contains both the free matrices and the nearly reducible matrices.

M3 - Report

BT - On free matrices

PB - Department of Mathematics, Technical University of Denmark

CY - København

ER -