The maximum distance problem and band sequences

A. Ben-Artzi*, R. L. Ellis, I. Gohberg, D. C. Lay

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

8 Scopus citations

Abstract

We solve the following problem. For 1 ≤ j, k ≤ n and |j - k| ≤ m, let ajk be a given complex number with akj = ājk. We wish to find linearly independent vectors x1,...,xn such that 〈xk, xj〉 = ajk for |j - k| ≤ m and such that the distance from xk to the linear span of x1,...,xk-1 is maximal for 2 ≤ k ≤ n. We construct and characterize all such sequences of vectors. Our solution leads naturally to the class of m-band sequences of vectors in an inner product space. We study these sequences and characterize their equivalence classes under unitary transformations.

Original languageEnglish
Pages (from-to)93-112
Number of pages20
JournalLinear Algebra and Its Applications
Volume87
Issue numberC
DOIs
StatePublished - Mar 1987

Funding

FundersFunder number
National Science Foundation

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