Matrices with Hyperbolical Krein Space Numerical Range
N. Bebiano, R. Lemos, G. Soares
TL;DR
This paper investigates matrices with hyperbolical Krein space numerical range, characterizing the shape for 2x2 matrices and certain classes, with conditions derived for low-dimensional tridiagonal matrices based on their entries.
Contribution
It provides necessary and sufficient conditions for low-dimensional tridiagonal matrices to have hyperbolical Krein space numerical range based solely on their entries.
Findings
Characterization of the hyperbolical shape in 2x2 matrices
Persistence of the shape in certain larger matrices
Explicit conditions for low-dimensional tridiagonal matrices
Abstract
This paper is devoted to matrices with hyperbolical Krein space numerical range. This shape characterizes the 2-by-2 case and persists for certain classes of matrices, independently of their size. Ne\-cessary and sufficient conditions for low dimensional tridiagonal matrices to have this shape are obtained only involving the matrix entries
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Taxonomy
TopicsMatrix Theory and Algorithms · Advanced Mathematical Theories and Applications