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A non-symmetric matrix with integer eigenvalues
Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.
Institute of Mathematical Statistics , University of Tartu , 50409 Tartu, Estonia.
2007 (English)In: Linear and Multilinear Algebra, ISSN 0308-1087, 1563-5139, Vol. 55, no 3, 239-247 p.Article in journal (Refereed) Published
Abstract [en]

A nonsymmetric N × N matrix with elements as certain simple functions of N distinct real or complex numbers r 1, r 2, …, rN is presented. The matrix is special due to its eigenvalues − the consecutive integers 0,1,2, …, N−1. Theorems are given establishing explicit expressions of the right and left eigenvectors and formulas for recursive calculation of the right eigenvectors. A special case of the matrix has appeared in sampling theory where its right eigenvectors, if properly normalized, give the inclusion probabilities of the conditional Poisson sampling design.

Place, publisher, year, edition, pages
Taylor & Francis Group, 2007. Vol. 55, no 3, 239-247 p.
National Category
Algebra and Logic
URN: urn:nbn:se:umu:diva-7762DOI: 10.1080/03081080600906455OAI: diva2:147433
Available from: 2008-01-11 Created: 2008-01-11 Last updated: 2014-03-19Bibliographically approved

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Bondesson, Lennart
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Department of Mathematics and Mathematical Statistics
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