An efficient algorithm is developed for determining the greatest common left divisor (GCLD) of two polynomial matrices. Knowing this divisor allows for several immediate applications. In coding theory, a noncatastrophic convolutional encoder can be derived from an arbitrary one. In systems theory, irreducible matrix fraction descriptions of transfer function matrices can be found. In linear algebra, the greatest common divisor can be seen as a basis for a free module generated by the columns of the matrices. The approach taken is based on recent ideas from systems theory. A minimal state space realization is obtained with minimal calculations, and from this the controllability matrix is analyzed to produce the GCLD. It will be shown that the derived algorithm is a natural extension of the Euclidean algorithm to the matrix case.

## ZORA Wartung

ZORA's new graphical user interface has been launched. For further infos take a look at Open Access Blog 'New Look & Feel – ZORA goes mobile'.

Allen, B; Rosenthal, J (1999). *A matrix Euclidean algorithm induced by state space realization.* Linear Algebra and its Applications, 288(1-3):105-121.

## Abstract

An efficient algorithm is developed for determining the greatest common left divisor (GCLD) of two polynomial matrices. Knowing this divisor allows for several immediate applications. In coding theory, a noncatastrophic convolutional encoder can be derived from an arbitrary one. In systems theory, irreducible matrix fraction descriptions of transfer function matrices can be found. In linear algebra, the greatest common divisor can be seen as a basis for a free module generated by the columns of the matrices. The approach taken is based on recent ideas from systems theory. A minimal state space realization is obtained with minimal calculations, and from this the controllability matrix is analyzed to produce the GCLD. It will be shown that the derived algorithm is a natural extension of the Euclidean algorithm to the matrix case.

## Citations

## Altmetrics

## Downloads

## Additional indexing

Item Type: | Journal Article, refereed, original work |
---|---|

Communities & Collections: | 07 Faculty of Science > Institute of Mathematics |

Dewey Decimal Classification: | 510 Mathematics |

Language: | English |

Date: | 1999 |

Deposited On: | 11 Mar 2010 14:54 |

Last Modified: | 05 Apr 2016 13:26 |

Publisher: | Elsevier |

ISSN: | 0024-3795 |

Publisher DOI: | 10.1016/S0024-3795(98)10186-6 |

## Download

TrendTerms displays relevant terms of the abstract of this publication and related documents on a map. The terms and their relations were extracted from ZORA using word statistics. Their timelines are taken from ZORA as well. The bubble size of a term is proportional to the number of documents where the term occurs. Red, orange, yellow and green colors are used for terms that occur in the current document; red indicates high interlinkedness of a term with other terms, orange, yellow and green decreasing interlinkedness. Blue is used for terms that have a relation with the terms in this document, but occur in other documents.

You can navigate and zoom the map. Mouse-hovering a term displays its timeline, clicking it yields the associated documents.