Hilbert Space
★★★★☆Undergraduate
📖Definition
Complete space with inner product. Infinite-dimensional generalization of Euclidean space
📐Formulas
⟨x, y⟩ = ⟨y, x⟩̄ (conjugate symmetry)
⟨x, x⟩ ≥ 0
||x|| = √⟨x, x⟩
Orthonormal basis: ⟨eᵢ, eⱼ⟩ = δᵢⱼ
✏️Examples
예제 1
L²(ℝ)
예제 2
ℓ²
예제 3
Quantum state space
⚡Applications
Quantum mechanics
Fourier analysis
Signal processing
🔗Related Documents
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