Day 243: Projections and Orthogonal Decomposition

Learning Objectives

• •**Define** projection operators and orthogonal projections
• •**Prove** the projection theorem: closed subspaces have unique orthogonal projections
• •**Characterize** orthogonal projections as $P^2 = P = P^\dagger$
• •**Decompose** Hilbert spaces as direct sums via projections
• •**Compute** projections onto various subspaces
• •**Connect** projections to quantum measurement and state collapse

Today's Schedule (7 hours)