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Journals / Eskişehir Osmangazi Üniversitesi Mühendislik Mimarlık Fakültesi Dergisi / 1996 / Cilt: 9 - Sayı: 1

A tutorial on the singular value decomposition

Tekil değer ayrıştırmaya genel bakış

Abdurrahman KARAMANCIOĞLU
Can ÖZDEMİR
Pages
1–12
Publication Date
2022-10-18
DOI
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AI Summary & Key Takeaways

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

In the last section we treat a special problem where action of the matrix A is restricted to a given subspace.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:An m x n real matrix A can be factored as; $UWV^T$ y where U and V are orthonormal, and W is upper left diagonal.
📊
Key Findings & Data:This factorization is c&lled Singular Value Decomposition (SVDJ.
💡
Conclusion & Impact:In the last section we treat a special problem where action of the matrix A is restricted to a given subspace.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Domain Parameters

Abstract

An m x n real matrix A can be factored as; $UWV^T$ y where U and V are orthonormal, and W is upper left diagonal. This factorization is c&lled Singular Value Decomposition (SVDJ. The matrices U, W, and V are useful in characterizing the matrix A. In this manuscript geometric characterizations are emphasized. Geometric characterizations are analyzed in terms of subspaces, matrix scaling, and norms. We also present a numerical viewpoint for SVD in order to keep the material self-contained. In the last section we treat a special problem where action of the matrix A is restricted to a given subspace.

Özet

An m x n real matrix A can be factored as; $UWV^T$ y where U and V are orthonormal, and W is upper left diagonal. This factorization is c&lled Singular Value Decomposition (SVDJ. The matrices U, W, and V are useful in characterizing the matrix A. In this manuscript geometric characterizations are emphasized. Geometric characterizations are analyzed in terms of subspaces, matrix scaling, and norms. We also present a numerical viewpoint for SVD in order to keep the material self-contained. In the last section we treat a special problem where action of the matrix A is restricted to a given subspace.

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Cite This Article

KARAMANCIOĞLU, A., ÖZDEMİR, C. (2022). A tutorial on the singular value decomposition. Eskişehir Osmangazi Üniversitesi Mühendislik Mimarlık Fakültesi Dergisi, Cilt: 9 - Sayı: 1, 1–12. https://ajindex.com/articles/586117

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References (2)

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