Bevilacqua, Roberto and Del Corso, Gianna M. (2012) *A Condensed Representation of Almost Normal Matrices.* Technical Report del Dipartimento di Informatica . Università di Pisa, Pisa, IT.

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## Abstract

In this paper we study the structure of almost normal matrices, that is the matrices for which there exists a rank-one matrix $C$ such that $A^HA-AA^H=CA-AC$. Necessary and sufficient conditions for a matrix to belong to the class are given and a canonical representation as a block tridiagonal matrix is shown. The approach is constructive and in the paper it is explained how, starting from a $1\times 1$ or $2\times 2$ matrix we can generate almost normal matrices. Moreover, given an $n\times n$ almost normal matrix we can compute the block tridiagonal representation with a finite procedure.<br /><br />

Item Type: | Book |
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Uncontrolled Keywords: | Perturbation of normal matrices, canonical representation |

Subjects: | Area01 - Scienze matematiche e informatiche > INF/01 - Informatica |

Divisions: | Dipartimenti (until 2012) > DIPARTIMENTO DI INFORMATICA |

Depositing User: | dott.ssa Sandra Faita |

Date Deposited: | 04 Nov 2014 16:04 |

Last Modified: | 04 Nov 2014 16:04 |

URI: | http://eprints.adm.unipi.it/id/eprint/2294 |

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