Krein Space Numerical Range of Block Matrices -- a Unified Approach to the Hyperbolic Case

Q: What type of study is this?

This is a Quantitative Study study.

Natália Bebiano; R. Lemos; G. Soares

doi:10.48550/arxiv.2508.12039

August 16, 2025Open Access

Krein Space Numerical Range of Block Matrices -- a Unified Approach to the Hyperbolic Case

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Key Points

The study identifies a unified approach to understand the numerical range of block matrices effectively.
This approach derives established and new results, particularly focusing on hyperbolic shapes in numerical range.
We focus on $2$-by-$2$ block matrices with specific diagonal blocks, utilizing hyperbolas as boundary curves.
The findings may enhance the understanding of Krein space numerical ranges in various mathematical contexts.

Implication

This investigation reveals the numerical range shape of block matrices, suggesting a unified method for hyperbolic cases.

Abstract

In this paper, we investigate the Krein space numerical range of $2$-by-$2$ block matrices, with diagonal blocks as scalar multiples of the identity. For these matrices, we specifically investigate the cases when the respective boundary generating curves consist of hyperbolas. This provides a unified approach to derive established and new results concerning the numerical range hyperbolic shape.

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Cite This Study

Bebiano et al. (2025) studied this question.

synapsesocial.com/papers/68d6e1978b2b6861e4c403b5 https://doi.org/10.48550/arxiv.2508.12039

View Full Paper

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Krein Space Numerical Range of Block Matrices -- a Unified Approach to the Hyperbolic Case

Key Points

Implication

Abstract

Discussion

Cite This Study

Krein Space Numerical Range of Block Matrices -- a Unified Approach to the Hyperbolic Case

Key Points

Implication

Abstract

Discussion

Cite This Study

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