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Quantum Engineering Year 0: Mathematical Foundations Month 5Day 120

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Year 0·Month 5·Week 2

Day 120: Singular Value Decomposition — The Ultimate Matrix Factorization

Day 120 of 2,016~12 min read

Learning Objectives

•State and prove the Singular Value Decomposition theorem
•Compute SVD for small matrices by hand
•Understand the geometric interpretation of SVD
•Relate SVD to eigendecomposition
•Apply SVD to matrix approximation and rank
•Connect SVD to quantum state analysis

Today's Schedule (7 hours)

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On this page

1 Motivation Why SVD 2 The SVD Theorem 3 Singular Values and Vectors 4 Proof Outline 5 Reduced SVD Compact Form 6 Geometric Interpretation 7 Properties of Singular Values 8 Low-Rank Approximation Quantum Mechanics Connection SVD and Quantum States Quantum Channels and SVD Fidelity and Singular Values

Day 119Day 120 of 2,016Day 121