On sufficient conditions for the total positivity and for the multiple positivity of matrices
Katkova, Olga M. · Vishnyakova, Anna M.
الأصل · EN
The following theorem is proved: Suppose M = (aᵢ,ⱼ) be a k × k matrix with positive entries and aᵢ,ⱼaᵢ₊₁,ⱼ₊₁ > 4 ² πk+1 aᵢ,ⱼ₊₁aᵢ₊₁,ⱼ (1 ≤ i ≤ k-1, 1 ≤ j ≤ k-1). Then M > 0. The constant 4 ² πk+1 in this Theorem is sharp. A few other results concerning totally positive and multiply positive matrices are obtained. Keywords: Multiply positive matrix; Totally positive matrix; Strictly totally positive matrix; Toeplitz matrix; Hankel matrix; Pólya frequency sequence.
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