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Orthogonality of matrices and some distance problems

✍ Scribed by Rajendra Bhatia; Peter Šemrl

Publisher
Elsevier Science
Year
1999
Tongue
English
Weight
348 KB
Volume
287
Category
Article
ISSN
0024-3795

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✦ Synopsis

If A and B are matrices such that IIA + zBII ~ IIA II for all complex numbers z, then A is said to be orthogonal to B. We find necessary and sufficient conditions for this to be the case. Some applications and generalisations are also discussed.

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Methods for constructing distance matric
Methods for constructing distance matrices and the inverse eigenvalue problem
✍ Thomas L. Hayden; Robert Reams; James Wells 📂 Article 📅 1999 🏛 Elsevier Science 🌐 English ⚖ 143 KB

Let h 1 P R kÂk and h 2 P R lÂl be two distance matrices. We provide necessary conditions on P R kÂl in order that be a distance matrix. We then show that it is always possible to border an n  n distance matrix, with certain scalar multiples of its Perron eigenvector, to construct an n 1  n 1 dis