Unveiling the Roots of Matrices - A Generalization and Field Extension of the Square Root of Matrices

2023 Spring Symposium

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Overview

In this poster, I and Rongyao explore and investigate advanced topics in linear algebra. Specifically, we first prove the Theorem: Any positive semi-definite symmetric real matrix has a unique positive semi-definite symmetric square root by polynomial matrices. Then we give a generalization from field ℝ to ℂ, and from square root to k-th root. Finally, we demonstrate the Theorem: Any invertible complex matrix has a k-th root by Jordan Canonical Form and Taylor Expansion. Our proofs’ validity and theorems’ value are considered and discussed. These topics have significant applications in the field of Algebra and Lie Theory. You can check our poster here. If you have any question, idea or seeking collaboration with us, feel free to contact me through email at kl4747@nyu.edu.

Presentation

I attended the NYUSH 2023 Fall Symposium to present the results of this research. Below are some pictures of the presentation.