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Quantum Engineering Year 0: Mathematical Foundations Month 4Day 101

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Year 0·Month 4·Week 3

Day 101: Diagonalization

Day 101 of 2,016~13 min read

Learning Objectives

•State the diagonalizability criterion
•Find the diagonalizing matrix P and diagonal matrix D
•Use diagonalization to compute matrix powers
•Understand why some matrices aren't diagonalizable
•Apply diagonalization to solve systems of ODEs
•Connect to quantum mechanics: diagonal Hamiltonians

Today's Schedule (7 hours)

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On this page

1 The Big Picture Why Diagonalize 2 Similarity and Diagonalization 3 The Diagonalization Theorem 4 Diagonalizability Criteria 5 Computing Matrix Powers 6 Matrix Exponential via Diagonalization 7 Non-Diagonalizable Defective Matrices Quantum Mechanics Connection Diagonal Hamiltonians Time Evolution Stationary States General State Evolution Measurement Basis

Day 100Day 101 of 2,016Day 102