On a matrix with integer eigenvalues and its relation to conditional Poisson sampling

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dc.contributor.authorBondesson, L.
dc.contributor.authorTraat, I.
dc.date.accessioned2013-05-15T21:04:08Z
dc.date.available2013-05-15T21:04:08Z
dc.date.issued2005
dc.description.abstractA special non-symmetric N × N matrix with eigenvalues 0, 1, 2, . . . ,N − 1 is presented. The matrix appears in sampling theory. Its right eigenvectors, if properly normalized, give the inclusion probabilities of the Conditional Poisson design (for all different fixed sample sizes). The explicit expressions for the right eigenvectors become complicated for N large. Nevertheless, the left eigenvectors have a simple analytic form. An inversion of the left eigenvector matrix produces the right eigenvectors − the inclusion probabilities. Finally, a more general matrix with similar properties is defined and expressions for its left and right eigenvectors are derived.en
dc.identifier.citationBondesson, L., Traat, I. (2005), On a matrix with integer eigenvalues and its relation to conditional Poisson sampling, Research Letters in the Information and Mathematical Sciences, 8, 155-163en
dc.identifier.issn1175-2777
dc.identifier.urihttp://hdl.handle.net/10179/4460
dc.language.isoenen
dc.publisherMassey Universityen
dc.subjectEigenvectoren
dc.subjectMatrix (mathematics)en
dc.subjectPoisson samplingen
dc.titleOn a matrix with integer eigenvalues and its relation to conditional Poisson samplingen
dc.typeArticleen
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