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Journals / Turkish Journal of Mathematics and Computer Science / 2021 / Cilt: 13 - Sayı: 1

Geometric Interpretation and Manifold Structure of Markov Matrices

Bülent Karakaş
Şenay Baydaş
Pages
14–18
Publication Date
2022-11-02
DOI
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AI Summary & Key Takeaways

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⚡ TL;DR(Too Long; Didn't Read)

In addition, this paper presents the set of Markov matrices is drawable, and this gives geometrical interpretation to Markov matrices.For the proof, we use the one-to-one corresponding among $n times n$ Markov matrices, the solution of linear equation system from derived Markov property, and the set of $(n-1)$-polytopes.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:In probability theory and statistics, the term Markov property refers to the memoryless property of a stochastic process.
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Key Findings & Data:It is named after the Russian mathematician AndreyAndreyevichMarkov.
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Conclusion & Impact:In addition, this paper presents the set of Markov matrices is drawable, and this gives geometrical interpretation to Markov matrices.For the proof, we use the one-to-one corresponding among $n times n$ Markov matrices, the solution of linear equation system from derived Markov property, and the set of $(n-1)$-polytopes.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Domain Parameters

Abstract

In probability theory and statistics, the term Markov property refers to the memoryless property of a stochastic process. It is named after the Russian mathematician AndreyAndreyevichMarkov. Every Markov matrix gives a linear equation system, and the solution of this equation system gives us a subset of $mathbb{R}_{n}^{n}$. This paper presents the new manifold structure on the set of the Markov matrices. In addition, this paper presents the set of Markov matrices is drawable, and this gives geometrical interpretation to Markov matrices.For the proof, we use the one-to-one corresponding among $n times n$ Markov matrices, the solution of linear equation system from derived Markov property, and the set of $(n-1)$-polytopes.

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Cite This Article

Karakaş, B., Baydaş, Ş. (2022). Geometric Interpretation and Manifold Structure of Markov Matrices. Turkish Journal of Mathematics and Computer Science, Cilt: 13 - Sayı: 1, 14–18. https://ajindex.com/articles/609096

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References (8)

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