Day 241: Adjoint Operators

Learning Objectives

• •**Define** the adjoint operator using the inner product relation
• •**Prove** existence and uniqueness of the adjoint via the Riesz representation theorem
• •**Compute** adjoints for matrix operators, multiplication operators, and integral operators
• •**Verify** the fundamental properties: $(A+B)^\dagger = A^\dagger + B^\dagger$, $(AB)^\dagger = B^\dagger A^\dagger$
• •**Prove** the key identity $\|A^\dagger A\| = \|A\|^2$
• •**Connect** the adjoint to the Hermitian conjugate in quantum mechanics

Today's Schedule (7 hours)