On ray-nonsingular matrices
نویسندگان
چکیده
منابع مشابه
Extremal properties of ray-nonsingular matrices
A ray–nonsingular matrix is a square complex matrix, A, such that each complex matrix whose entries have the same arguments as the corresponding entries of A is nonsingular. Extremal properties of ray– nonsingular matrices are studied in this paper. Combinatorial and probabilistic arguments are used to prove that if the order of a ray– nonsingular matrix is at least 6, then it must contain a ze...
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A description is given of those ray-patterns, which will be called inverse closed ray-nonsingular, of complex matrices that contain invertible matrices only and are closed under inversion. Here, two n × n matrices are said to belong to the same ray-pattern if in each position either the entries of both matrices are zeros, or both entries are nonzero and their quotient is positive. Possible Jord...
متن کاملEla Non - Existence of 5 × 5 Full Ray - Nonsingular Matrices
An n × n complex matrix is full ray-nonsingular if it has no zero entries and every matrix obtained by changing the magnitudes of its entries is nonsingular. It is shown that a 5×5 full ray-nonsingular matrix does not exist. This, combined with earlier results, shows that there exists an n× n full ray-nonsingular matrix if and only if n ≤ 4.
متن کاملNon-existence of 5X5 full ray nonsingular matrices
An n × n complex matrix is full ray-nonsingular if it has no zero entries and every matrix obtained by changing the magnitudes of its entries is nonsingular. It is shown that a 5×5 full ray-nonsingular matrix does not exist. This, combined with earlier results, shows that there exists an n× n full ray-nonsingular matrix if and only if n ≤ 4.
متن کاملNew results on nonsingular power LCM matrices
Let e and n be positive integers and S = {x1, . . . , xn} be a set of n distinct positive integers. The n × n matrix having eth power [xi, xj ] of the least common multiple of xi and xj as its (i, j)-entry is called the eth power least common multiple (LCM) matrix on S, denoted by ([S]). The set S is said to be gcd closed (respectively, lcm closed) if (xi, xj) ∈ S (respectively, [xi, xj ] ∈ S) ...
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ژورنال
عنوان ژورنال: Linear Algebra and its Applications
سال: 2004
ISSN: 0024-3795
DOI: 10.1016/j.laa.2003.06.012