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 - https://www.scopus.com/pages/publications/45949119764
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 -