Spectral Theorem
★★★★★Graduate+
📖Definition
Self-adjoint (Hermitian) operators can be diagonalized via eigenvalues and eigenvectors
📐Formulas
T = ∫λ dE_λ (spectral decomposition)
Finite dim: T = Σλᵢ Pᵢ
σ(T) ⊂ ℝ (self-adjoint)
✏️Examples
예제 1
Symmetric matrices
예제 2
Quantum observables
예제 3
Sturm-Liouville problems
⚡Applications
Quantum mechanics
Differential equations
Vibration analysis
🔗Related Documents
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