An algorithmic approach to simultaneous triangularization

C. Dubi

doi:10.1016/j.laa.2008.05.037

An algorithmic approach to simultaneous triangularization

C. Dubi

Research output: Contribution to journal › Article › peer-review

16 Scopus citations

Abstract

We present and prove the validity of an algorithm constructing a simultaneous triangularization of a set on N matrices in C^{n × n}. To do so, we first prove that if a set of matrices has a common block decomposition, then the set of matrices has a simultaneous triangularization if and only if the blocks on the diagonal have a simultaneous triangularization.

Original language	English
Pages (from-to)	2975-2981
Number of pages	7
Journal	Linear Algebra and Its Applications
Volume	430
Issue number	11-12
DOIs	https://doi.org/10.1016/j.laa.2008.05.037
State	Published - 1 Jun 2009
Externally published	Yes

Keywords

Common eigenvector
Lie Algebra
Simultaneous triangularization

ASJC Scopus subject areas

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

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10.1016/j.laa.2008.05.037

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title = "An algorithmic approach to simultaneous triangularization",

abstract = "We present and prove the validity of an algorithm constructing a simultaneous triangularization of a set on N matrices in Cn × n. To do so, we first prove that if a set of matrices has a common block decomposition, then the set of matrices has a simultaneous triangularization if and only if the blocks on the diagonal have a simultaneous triangularization.",

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year = "2009",

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T1 - An algorithmic approach to simultaneous triangularization

AU - Dubi, C.

PY - 2009/6/1

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N2 - We present and prove the validity of an algorithm constructing a simultaneous triangularization of a set on N matrices in Cn × n. To do so, we first prove that if a set of matrices has a common block decomposition, then the set of matrices has a simultaneous triangularization if and only if the blocks on the diagonal have a simultaneous triangularization.

AB - We present and prove the validity of an algorithm constructing a simultaneous triangularization of a set on N matrices in Cn × n. To do so, we first prove that if a set of matrices has a common block decomposition, then the set of matrices has a simultaneous triangularization if and only if the blocks on the diagonal have a simultaneous triangularization.

KW - Common eigenvector

KW - Lie Algebra

KW - Simultaneous triangularization

UR - https://www.scopus.com/pages/publications/64649084927

U2 - 10.1016/j.laa.2008.05.037

DO - 10.1016/j.laa.2008.05.037

M3 - Article

AN - SCOPUS:64649084927

SN - 0024-3795

VL - 430

SP - 2975

EP - 2981

JO - Linear Algebra and Its Applications

JF - Linear Algebra and Its Applications

IS - 11-12

ER -

An algorithmic approach to simultaneous triangularization

Abstract

Keywords

ASJC Scopus subject areas

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