- 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
Read more about this topic: List Of Functional Analysis Topics
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