article · Proceedings of the American Mathematical Society · 1985
Matrix completion theorems
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Abstract
Let Rbea principal ideal ring, M, " the set of / X n matrices over R. The following results are proved :(a) Let D e M" ".Then the least nonnegative integer t such that a matrix [% p] exists which belongs to GL(n + t, R) is t = n -p, where p is the number of invariant factors of D equal to 1.(b) Any primitive element of M 2" may be completed to a 2n X 2n symplectic matrix.(c) If A, B s M" " are such that [A, B] is primitive and AB is symmetric, then [A, B] may be completed to a 2 X In symplectic matrix.(d) If A e M, ,, B e M, "_, are such that [A, B] is primitive and A is symmetric, then [A, B] may be completed to a symmetric element of SL(, R), provided that 1 t h/3.(e) If n > 3, then any primitive element of Mln occurs as the first row of the commutator of two elements of SL(n, R).Basic Result.Let a be a primitive element of Mx n.Then an element ofGL(n, R) exists whose first row is a.If n ^ 2, an element ofSL(n, R) exists whose first row is a.
Cite this paper
Newman, M. (1985). Matrix completion theorems. Proceedings of the American Mathematical Society, 94(1), 39. https://doi.org/10.1090/s0002-9939-1985-0781052-8
Newman, Morris. “Matrix completion theorems.” Proceedings of the American Mathematical Society, vol. 94, no. 1, 1985, p. 39, https://doi.org/10.1090/s0002-9939-1985-0781052-8.
Newman, Morris. 1985. “Matrix completion theorems.” Proceedings of the American Mathematical Society 94 (1): 39. https://doi.org/10.1090/s0002-9939-1985-0781052-8.
Newman, M. (1985) ‘Matrix completion theorems’, Proceedings of the American Mathematical Society, 94(1), p. 39. Available at: https://doi.org/10.1090/s0002-9939-1985-0781052-8.
@article{newman1985matrix,
title = {{Matrix completion theorems}},
author = {Newman, Morris},
journal = {Proceedings of the American Mathematical Society},
volume = {94},
number = {1},
pages = {39},
year = {1985},
doi = {10.1090/s0002-9939-1985-0781052-8}
}Made from the index record. Check names, capitalisation and page numbers against the paper. Need another style? AI for Research has over 10,000.