A note on infinite extreme correlation matrices

J. Kiukas; J. P. Pellonpää

doi:10.1016/j.laa.2007.12.001

A note on infinite extreme correlation matrices

J. Kiukas, J. P. Pellonpää

University of Turku

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

Abstract

We give a characterization for the extreme points of the convex set of correlation matrices with a countable index set. A Hermitian matrix is called a correlation matrix if it is positive semidefinite with unit diagonal entries. Using the characterization we show that there exist extreme points of any rank.

Original language	English
Pages (from-to)	2501-2508
Number of pages	8
Journal	Linear Algebra and Its Applications
Volume	428
Issue number	11-12
Early online date	24 Jan 2008
DOIs	https://doi.org/10.1016/j.laa.2007.12.001
Publication status	Published - 01 Jun 2008
Externally published	Yes

Keywords

Extreme point
Infinite correlation matrix
Rank

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10.1016/j.laa.2007.12.001

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title = "A note on infinite extreme correlation matrices",

abstract = "We give a characterization for the extreme points of the convex set of correlation matrices with a countable index set. A Hermitian matrix is called a correlation matrix if it is positive semidefinite with unit diagonal entries. Using the characterization we show that there exist extreme points of any rank.",

keywords = "Extreme point, Infinite correlation matrix, Rank",

author = "J. Kiukas and Pellonp{\"a}{\"a}, {J. P.}",

note = "Funding Information: The authors thank Drs. Pekka Lahti and Kari Ylinen for fruitful discussions. One of us (J.K.) was supported by Finnish Cultural Foundation. Copyright: Copyright 2008 Elsevier B.V., All rights reserved.",

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N1 - Funding Information: The authors thank Drs. Pekka Lahti and Kari Ylinen for fruitful discussions. One of us (J.K.) was supported by Finnish Cultural Foundation. Copyright: Copyright 2008 Elsevier B.V., All rights reserved.

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Y1 - 2008/6/1

N2 - We give a characterization for the extreme points of the convex set of correlation matrices with a countable index set. A Hermitian matrix is called a correlation matrix if it is positive semidefinite with unit diagonal entries. Using the characterization we show that there exist extreme points of any rank.

AB - We give a characterization for the extreme points of the convex set of correlation matrices with a countable index set. A Hermitian matrix is called a correlation matrix if it is positive semidefinite with unit diagonal entries. Using the characterization we show that there exist extreme points of any rank.

KW - Extreme point

KW - Infinite correlation matrix

KW - Rank

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U2 - 10.1016/j.laa.2007.12.001

DO - 10.1016/j.laa.2007.12.001

M3 - Article

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SP - 2501

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JO - Linear Algebra and Its Applications

JF - Linear Algebra and Its Applications

IS - 11-12

ER -

A note on infinite extreme correlation matrices

Abstract

Keywords

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