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- W2028993047 abstract "In 1958, Karl Goldberg proved the following: Theorem G. Suppose A=(aij) is an n×n matrix over the complex field, with the following properties: (1) aijaji⩾0 for i,j=1,2,…,n, and (2) ai1i2ai2i3⋯aisii=ai2i1ai3i2⋯ai1is for all s=1,2,…,n and it=1,2,…,n. Then A has only real characteristic values. Definition. Let Gn denote the class of n×n matrices over C, the complex field, which satisfy the Goldberg conditions (1) and (2). We investigate some properties of class G related to the following topics: Schur complements, weak sign symmetry, and inequalities due to Oppenheim for positive definite matrices, and an analogue due to Markham for tridiagonal, oscillatory matrices." @default.
- W2028993047 created "2016-06-24" @default.
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- W2028993047 date "1981-08-01" @default.
- W2028993047 modified "2023-09-27" @default.
- W2028993047 title "Class G, and a unification problem" @default.
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- W2028993047 doi "https://doi.org/10.1016/0024-3795(81)90303-7" @default.
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