منابع مشابه
Maximum exponent of boolean circulant matrices with constant number of nonzero entries in its generating vector
It is well-known that the maximum exponent that an n-by-n boolean primitive circulant matrix can attain is n− 1. In this paper, we find the maximum exponent that n-by-n boolean primitive circulant matrices with constant number of nonzero entries in its generating vector can attain. We also give matrices attaining such exponents. Solving this problem we also solve two equivalent problems: 1) fin...
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It is well-known that the maximum exponent that an n-by-n boolean primitive circulant matrix can attain is n − 1. In this paper, we find the maximum exponent attained by n-by-n boolean primitive circulant matrices with constant number of nonzero entries in their generating vector. We also give matrices attaining such exponents. Solving this problem we also solve two equivalent problems: 1) find...
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We discuss an extension of the almost Hadamard matrix formalism, to the case of complex matrices. Quite surprisingly, the situation here is very different from the one in the real case, and our conjectural conclusion is that there should be no such matrices, besides the usual Hadamard ones. We verify this conjecture in a number of situations, and notably for most of the known examples of real a...
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An L-matrix is a matrix whose off-diagonal entries belong to a set L, and whose diagonal is zero. Let N(r, L) be the maximum size of a square L-matrix of rank at most r. Many applications of linear algebra in extremal combinatorics involve a bound on N(r, L). We review some of these applications, and prove several new results on N(r, L). In particular, we classify the sets L for which N(r, L) i...
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ژورنال
عنوان ژورنال: Linear Algebra and its Applications
سال: 1991
ISSN: 0024-3795
DOI: 10.1016/0024-3795(91)90023-p