Off-diagonal elements of normal matrices
نویسندگان
چکیده
منابع مشابه
Existence of Matrices with Prescribed Off-Diagonal Block Element Sums
Necessary and sufficient conditions are proven for the existence of a square matrix, over an arbitrary field, such that for every principal submatrix the sum of the elements in the row complement of the submatrix is prescribed. The problem is solved in the cases where the positions of the nonzero elements of A are contained in a given set of positions, and where there is no restriction on the p...
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Similar to the well known Schur Horn theorem that characterizes the relationship between the diagonal entries and the eigenvalues of a Hermitian matrix the Sing Thompson theorem characterizes the relationship between the diagonal en tries and the singular values of an arbitrary matrix It is noted in this paper that based on the induction principle such a matrix can be constructed numerically by...
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Experience shows that there is a strong parallel between metrization theory for compact spaces and for linearly ordered spaces in terms of diagonal conditions. Recent theorems of Gruenhage, Pelant, Kombarov, and Stepanova have described metrizability of compact (and related) spaces in terms of the offdiagonal behavior of those spaces, i.e., in terms of properties of X −∆. In this paper, we show...
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Systems of linear differential equations with constant coefficients, as well as Lotka–Volterra equations, with delays in the off–diagonal terms are considered. Such systems are shown to be asymptotically stable for any choice of delays if and only if the matrix has a negative weakly dominant diagonal.
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For simplicity, we adopt the following rules: i, j, m, n, k denote natural numbers, x denotes a set, K denotes a field, a, a1, a2 denote elements of K, D denotes a non empty set, d, d1, d2 denote elements of D, M , M1, M2 denote matrices over D, A, A1, A2, B1, B2 denote matrices over K, and f , g denote finite sequences of elements of N. One can prove the following propositions: (1) Let K be a ...
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ژورنال
عنوان ژورنال: Journal of Research of the National Bureau of Standards, Section B: Mathematical Sciences
سال: 1977
ISSN: 0098-8979
DOI: 10.6028/jres.081b.007