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Journals / Hacettepe Journal of Mathematics and Statistics / 2021 / Cilt: 50 - Sayı: 1

On the trace of powers of square matrices

Kailash M. Patil
Pages
14–23
Publication Date
2022-10-18
DOI
—
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AI Summary & Key Takeaways

AI Insight
⚡ TL;DR(Too Long; Didn't Read)

As a consequence, we also demonstrate the formula for trace of negative powers of a matrix.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:Using Cayley-Hamilton equation for matrices, we obtain a simple formula for trace of powers of a square matrix.
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Key Findings & Data:The formula becomes simpler in particular cases.
💡
Conclusion & Impact:As a consequence, we also demonstrate the formula for trace of negative powers of a matrix.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:trace of a matrix · powers of a matrix · Cayley-Hamilton theorem

Abstract

Using Cayley-Hamilton equation for matrices, we obtain a simple formula for trace of powers of a square matrix. The formula becomes simpler in particular cases. As a consequence, we also demonstrate the formula for trace of negative powers of a matrix.

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Cite This Article

Patil, K. M. (2022). On the trace of powers of square matrices. Hacettepe Journal of Mathematics and Statistics, Cilt: 50 - Sayı: 1, 14–23. https://ajindex.com/articles/530005

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References (6)

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