Characteristically Near Stable Vector Fields in the Polar Complex Plane

Year 2025, Volume: 8 Issue: 2, 117 - 124, 01.07.2025

James F. Peters , Enze Cui

https://doi.org/10.33434/cams.1660609

Abstract

This paper introduces results for characteristically proximal vector fields that are stable or non-stable in the polar complex plane $\mathbb{C}$. All characteristic vectors (aka eigenvectors) emanate from the same fixed point in $\mathbb{C}$, namely, 0. Stable characteristic vector fields satisfy an extension of the Krantz stability condition, namely, the maximal eigenvalue of a stable system lies within or on the boundary of the unit circle in $\mathbb{C}$. An application is given for stable vector fields detected in motion waveforms in infrared video frames. AI is used to separate the changing from the unchanging parts of each video frame.

Keywords

Characteristic , Complex Plane , Eigenvalue , Eigenvector , Proximity , Stability

Ethical Statement

This paper has not been submitted to any other publication.

Supporting Institution

University of Manitoba, Canada

Thanks

Many thanks for considering this paper for publication in the CAMS journal.

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