Day 233: Inner Product Spaces

Learning Objectives

• •**Define** an inner product and verify the inner product axioms
• •**Prove** the Cauchy-Schwarz inequality and understand its geometric meaning
• •**Show** that every inner product induces a norm
• •**State and apply** the polarization identity
• •**Prove** the parallelogram law and understand why it characterizes inner product spaces
• •**Connect** inner products to quantum mechanical probability amplitudes

Today's Schedule (7 hours)