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Level numbers of a bounded linear operator between normed linear spaces and singular value decomposition revisited
Linear and Multilinear Algebra ( IF 1.1 ) Pub Date : 2020-12-08
Debmalya Sain, Saikat Roy, Ryotaro Tanaka

ABSTRACT

We introduce the notion of level numbers of a bounded linear operator between normed linear spaces, as a generalization of the singular values of an operator between inner product spaces. We study the geometric and the analytic properties of the level numbers, in connection with Birkhoff–James orthogonality and norm optimization problems. We also illustrate the similarities and the differences between the level numbers and the singular values of an operator. As an application of the present study, we obtain a new and elementary approach to the singular value decomposition of matrices.



中文翻译:

重新探讨赋范线性空间与奇异值分解之间有界线性算子的能级数

摘要

我们引入范数线性空间之间有界线性算子的级数的概念,作为内部乘积空间之间算子奇异值的概括。我们结合Birkhoff-James正交性和范数优化问题研究了级数的几何和解析性质。我们还说明了级别数和运算符的奇异值之间的相似之处和不同之处。作为本研究的应用,我们获得了矩阵奇异值分解的一种新的基本方法。

更新日期:2020-12-08
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