关于元素为[−a, a]的单位下三角矩阵的最小奇异值

IF 0.8 Q2 MATHEMATICS

Special Matrices Pub Date : 2021-01-01 DOI:10.1515/spma-2020-0139

E. Altinisik

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引用次数: 0

摘要

摘要给定实数a≥1，设Kn（a）是区间[−a，a]内所有n×n个单位下三角矩阵的集合。用λn（·）表示给定矩阵的最小特征值，设cn（a）=min{λn（YYT）:Y∈Kn（a）}。则cn（a）\sqrt｛c_n｝\left（a\right）｝是Kn（a）中最小的奇异值。我们找到所有最小化矩阵。此外，我们还研究了cn（a）作为n的渐近性态→ ∞. 最后，将[−a，a]替换为[a，b]，a≤0本文章由计算机程序翻译，如有差异，请以英文原文为准。

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On the smallest singular value in the class of unit lower triangular matrices with entries in [−a, a]

Abstract Given a real number a ≥ 1, let Kn(a) be the set of all n × n unit lower triangular matrices with each element in the interval [−a, a]. Denoting by λn(·) the smallest eigenvalue of a given matrix, let cn(a) = min {λ n(YYT) : Y ∈ Kn(a)}. Then cn(a)\sqrt {{c_n}\left( a \right)} is the smallest singular value in Kn(a). We find all minimizing matrices. Moreover, we study the asymptotic behavior of cn(a) as n → ∞. Finally, replacing [−a, a] with [a, b], a ≤ 0 < b, we present an open question: Can our results be generalized in this extension?

来源期刊

Special Matrices MATHEMATICS-

CiteScore

1.10

自引率

20.00%

发文量

审稿时长

8 weeks

期刊介绍： Special Matrices publishes original articles of wide significance and originality in all areas of research involving structured matrices present in various branches of pure and applied mathematics and their noteworthy applications in physics, engineering, and other sciences. Special Matrices provides a hub for all researchers working across structured matrices to present their discoveries, and to be a forum for the discussion of the important issues in this vibrant area of matrix theory. Special Matrices brings together in one place major contributions to structured matrices and their applications. All the manuscripts are considered by originality, scientific importance and interest to a general mathematical audience. The journal also provides secure archiving by De Gruyter and the independent archiving service Portico.