TY - JOUR

T1 - The maximum distance problem and band sequences

AU - Ben-Artzi, A.

AU - Ellis, R. L.

AU - Gohberg, I.

AU - Lay, D. C.

N1 - Funding Information:
by an NSF Grant

PY - 1987/3

Y1 - 1987/3

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=45949119764&partnerID=8YFLogxK

U2 - 10.1016/0024-3795(87)90161-3

DO - 10.1016/0024-3795(87)90161-3

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AN - SCOPUS:45949119764

SN - 0024-3795

VL - 87

SP - 93

EP - 112

JO - Linear Algebra and Its Applications

JF - Linear Algebra and Its Applications

IS - C

ER -