A short proof of the elliptical range theorem
Gyula Lakos
TL;DR
This paper presents a concise proof of the elliptical range theorem, which characterizes the numerical range of 2x2 complex matrices, simplifying understanding of this fundamental result in matrix analysis.
Contribution
The paper provides a shorter, more accessible proof of the elliptical range theorem, enhancing clarity and pedagogical value compared to existing proofs.
Findings
Simplified proof of the elliptical range theorem
Clarification of the geometric properties of numerical ranges
Potential for improved teaching and understanding of matrix analysis
Abstract
A short proof of the elliptical range theorem concerning the numerical range of complex matrices is given.
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Taxonomy
TopicsMatrix Theory and Algorithms · Mathematical functions and polynomials · Mathematics and Applications