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Methods for constructing distance matrices and the inverse eigenvalue problem

โœ Scribed by Thomas L. Hayden; Robert Reams; James Wells

Publisher
Elsevier Science
Year
1999
Tongue
English
Weight
143 KB
Volume
295
Category
Article
ISSN
0024-3795

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โœฆ Synopsis

Let h 1 P R kร‚k and h 2 P R lร‚l be two distance matrices. We provide necessary conditions on P R kร‚l in order that

be a distance matrix. We then show that it is always possible to border an n ร‚ n distance matrix, with certain scalar multiples of its Perron eigenvector, to construct an n 1 ร‚ n 1 distance matrix. We also give necessary and sucient conditions for two principal distance matrix blocks h 1 and h 2 be used to form a distance matrix as above, where Z is a scalar multiple of a rank one matrix, formed from their Perron eigenvectors. Finally, we solve the inverse eigenvalue problem for distance matrices in certain special cases, including n 3Y 4Y 5Y 6, any n for which there exists a Hadamard matrix, and some other cases.

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