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Quantum Engineering Year 0: Mathematical Foundations Month 5Day 121

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Year 0·Month 5·Week 2

Day 121: SVD Applications — From Data Science to Quantum Mechanics

Day 121 of 2,016~12 min read

Learning Objectives

•Compute the Moore-Penrose pseudoinverse using SVD
•Solve least squares problems via SVD
•Apply Principal Component Analysis (PCA)
•Understand the polar decomposition
•Connect SVD to the Schmidt decomposition in quantum mechanics
•Apply SVD to quantum state analysis

Today's Schedule (7 hours)

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1 The Moore-Penrose Pseudoinverse 2 Least Squares via SVD 3 Principal Component Analysis PCA 4 Polar Decomposition via SVD 5 Matrix Norms and Condition Number Quantum Mechanics Connection The Schmidt Decomposition Connection to SVD Entanglement and Schmidt Rank Example Bell States Quantum State Tomography

Day 120Day 121 of 2,016Day 122