List of Functional Analysis Topics - Hilbert Space

  • Definite bilinear form
  • Euclidean space
  • Inner product space
  • Hilbert space
  • Parallelogram law
  • Orthonormal basis
  • Orthogonalization
  • Orthogonal complement
  • Gram–Schmidt process
  • Legendre polynomials
  • Matrices
    • Orthogonal matrix
    • Unitary matrix
    • Normal matrix, normal operator
    • Symmetric matrix
    • Hermitian operator self-adjoint operator, Hermitian adjoint
    • Eigenvector, eigenvalue, eigenfunction
    • Diagonal matrix
    • Shift operator
    • Hilbert matrix
  • Normal vector
  • Parseval's identity
  • Riesz representation theorem
  • Bra-ket notation
  • Spectral theorem, Spectral theory
  • Rayleigh quotient
  • Mercer's theorem
  • Reproducing kernel Hilbert space
  • Trace class
  • Min-max theorem
  • Rigged Hilbert space
  • Hellinger–Toeplitz theorem
  • Direct integral
  • Semi-Hilbert space

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    “For tribal man space was the uncontrollable mystery. For technological man it is time that occupies the same role.”
    —Marshall McLuhan (1911–1980)