Investigating the Numerical Range of Non Square Matrices
Aikaterini Aretaki, John Maroulas
TL;DR
This paper explores the concept of numerical range for rectangular matrices, introducing new definitions and properties, and extends the discussion to rank-k numerical ranges, contributing to the mathematical understanding of non-square matrices.
Contribution
It introduces two new definitions of numerical range for rectangular matrices and extends the concept to rank-k numerical ranges, expanding theoretical understanding.
Findings
Defined two types of numerical range for rectangular matrices
Established basic properties of these numerical ranges
Extended the concept to rank-k numerical ranges
Abstract
A presentation of numerical range for rectangular matrices is undertaken in this paper, introducing two different definitions and elaborating basic properties. Then we are extended to the treatment of rank-k numerical range.
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Taxonomy
TopicsMatrix Theory and Algorithms · Advanced Mathematical Theories and Applications · Advanced Optimization Algorithms Research