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Quantum Engineering Year 0: Mathematical Foundations Month 4Day 87

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Year 0·Month 4·Week 1

Day 87: Span and Spanning Sets

Day 87 of 2,016~16 min read

Learning Objectives

•Define the span of a set of vectors
•Determine if a set of vectors spans a given space
•Find the span of specific vector sets in ℝⁿ and ℂⁿ
•Understand span as the "smallest subspace containing" a set
•Connect span to systems of linear equations
•Relate span to superposition in quantum mechanics

Today's Schedule (7 hours)

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On this page

1 Definition of Span 2 Span is a Subspace 3 Fundamental Examples Example 1 Span in Example 2 Span of a single vector Example 3 Span might be smaller than expected Example 4 Span in 4 Spanning Sets 5 Testing if a Vector is in a Span 6 The Column Space 7 When Does a Set Span 8 Polynomial Spaces Quantum Mechanics Connection Superposition and Span Example Spin-12 Particle

Day 86Day 87 of 2,016Day 88