An angle metric through the notion of Grassmann representative

Grigoris I. Kalogeropoulos; Athanasios D. Karageorgos; Athanasios A. Pantelous

An angle metric through the notion of Grassmann representative

Grigoris I. Kalogeropoulos, Athanasios D. Karageorgos, Athanasios A. Pantelous

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

Abstract

The present paper has two main goals. Firstly, to introduce different metric topologies on the pencils (F, G) associated with autonomous singular (or regular) linear differential or difference systems. Secondly, to establish a new angle metric which is described by decomposable multi-vectors called Grassmann representatives (or Plücker coordinates) of the corresponding subspaces. A unified framework is provided by connecting the new results to known ones, thus aiding in the deeper understanding of various structural aspects of matrix pencils in system theory.

Original language	English
Pages (from-to)	108-116
Number of pages	9
Journal	Electronic Journal of Linear Algebra
Volume	18
Publication status	Published - Jan 2009
Externally published	Yes

Keywords

Angle metric
Exterior algebra
Grassmann manifold
Grassmann representative
Plücker coordinates

Cite this

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abstract = "The present paper has two main goals. Firstly, to introduce different metric topologies on the pencils (F, G) associated with autonomous singular (or regular) linear differential or difference systems. Secondly, to establish a new angle metric which is described by decomposable multi-vectors called Grassmann representatives (or Pl{\"u}cker coordinates) of the corresponding subspaces. A unified framework is provided by connecting the new results to known ones, thus aiding in the deeper understanding of various structural aspects of matrix pencils in system theory.",

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AU - Pantelous, Athanasios A.

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N2 - The present paper has two main goals. Firstly, to introduce different metric topologies on the pencils (F, G) associated with autonomous singular (or regular) linear differential or difference systems. Secondly, to establish a new angle metric which is described by decomposable multi-vectors called Grassmann representatives (or Plücker coordinates) of the corresponding subspaces. A unified framework is provided by connecting the new results to known ones, thus aiding in the deeper understanding of various structural aspects of matrix pencils in system theory.

AB - The present paper has two main goals. Firstly, to introduce different metric topologies on the pencils (F, G) associated with autonomous singular (or regular) linear differential or difference systems. Secondly, to establish a new angle metric which is described by decomposable multi-vectors called Grassmann representatives (or Plücker coordinates) of the corresponding subspaces. A unified framework is provided by connecting the new results to known ones, thus aiding in the deeper understanding of various structural aspects of matrix pencils in system theory.

KW - Angle metric

KW - Exterior algebra

KW - Grassmann manifold

KW - Grassmann representative

KW - Plücker coordinates

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VL - 18

SP - 108

EP - 116

JO - Electronic Journal of Linear Algebra

JF - Electronic Journal of Linear Algebra

ER -

An angle metric through the notion of Grassmann representative

Abstract

Keywords

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