On a Class of Singular Nonsymmetric Matrices with Nonnegative Integer Spectra

T. von Rosen; Dietrich von Rosen

On a Class of Singular Nonsymmetric Matrices with Nonnegative Integer Spectra

T. von Rosen
, Dietrich von Rosen

Department of Energy and Technology

Publication: Chapter in Book/Report/Conference proceeding › Conference paper in proceedings › peer-review

Abstract

This paper presents a simple derivation of eigenvalues, and left and right eigenvectors of a square nonsymmetric matrix that appears in sampling theory, and its properly normalized right eigenvectors give the inclusion probabilities. The proof is based on a special Vandermonde matrix.

Original language	English
Title of host publication	Algebraic methods in statistics and probability II : AMS Special Session Algebraic Methods in Statistics and Probability, March 27-29, 2009, University of Illinois at Urbana-Champaign, Champaign, IL
Publisher	American Mathematical Society
Pages	319-324
Number of pages	7
ISBN (Print)	978-0-8218-4891-3
Publication status	Published - 2010

Publication series

Series	Contemporary Mathematics
Number	516
Volume	516
ISSN	0271-4132

Keywords

Integer spectra
Vandermonde matrix
inverse Vandermonde matrix

Cite this

von Rosen, T. ; von Rosen, Dietrich. / On a Class of Singular Nonsymmetric Matrices with Nonnegative Integer Spectra. Algebraic methods in statistics and probability II : AMS Special Session Algebraic Methods in Statistics and Probability, March 27-29, 2009, University of Illinois at Urbana-Champaign, Champaign, IL. American Mathematical Society, 2010. pp. 319-324 (Contemporary Mathematics; No. 516, Vol. 516).

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von Rosen, T & von Rosen, D 2010, On a Class of Singular Nonsymmetric Matrices with Nonnegative Integer Spectra. in Algebraic methods in statistics and probability II : AMS Special Session Algebraic Methods in Statistics and Probability, March 27-29, 2009, University of Illinois at Urbana-Champaign, Champaign, IL. American Mathematical Society, Contemporary Mathematics, no. 516, vol. 516, pp. 319-324.

On a Class of Singular Nonsymmetric Matrices with Nonnegative Integer Spectra. / von Rosen, T.; von Rosen, Dietrich.
Algebraic methods in statistics and probability II : AMS Special Session Algebraic Methods in Statistics and Probability, March 27-29, 2009, University of Illinois at Urbana-Champaign, Champaign, IL. American Mathematical Society, 2010. p. 319-324 (Contemporary Mathematics; No. 516, Vol. 516).

Publication: Chapter in Book/Report/Conference proceeding › Conference paper in proceedings › peer-review

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AU - von Rosen, T.

AU - von Rosen, Dietrich

PY - 2010

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N2 - This paper presents a simple derivation of eigenvalues, and left and right eigenvectors of a square nonsymmetric matrix that appears in sampling theory, and its properly normalized right eigenvectors give the inclusion probabilities. The proof is based on a special Vandermonde matrix.

AB - This paper presents a simple derivation of eigenvalues, and left and right eigenvectors of a square nonsymmetric matrix that appears in sampling theory, and its properly normalized right eigenvectors give the inclusion probabilities. The proof is based on a special Vandermonde matrix.

KW - Integer spectra

KW - Vandermonde matrix

KW - inverse Vandermonde matrix

KW - Integer spectra

KW - Vandermonde matrix

KW - inverse Vandermonde matrix

UR - https://res.slu.se/id/publ/32943

M3 - Conference paper in proceedings

SN - 978-0-8218-4891-3

T3 - Contemporary Mathematics

SP - 319

EP - 324

BT - Algebraic methods in statistics and probability II : AMS Special Session Algebraic Methods in Statistics and Probability, March 27-29, 2009, University of Illinois at Urbana-Champaign, Champaign, IL

PB - American Mathematical Society

ER -

von Rosen T, von Rosen D. On a Class of Singular Nonsymmetric Matrices with Nonnegative Integer Spectra. In Algebraic methods in statistics and probability II : AMS Special Session Algebraic Methods in Statistics and Probability, March 27-29, 2009, University of Illinois at Urbana-Champaign, Champaign, IL. American Mathematical Society. 2010. p. 319-324. (Contemporary Mathematics; No. 516, Vol. 516).

On a Class of Singular Nonsymmetric Matrices with Nonnegative Integer Spectra

Abstract

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Keywords

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