Linear and multilinear algebra; matrix theory Inner product spaces Concept
Orthonormal basis
Summary
An orthonormal basis of a finite-dimensional inner product space is a basis whose vectors have length one and are pairwise orthogonal.
Where this leads
38 pages build on this one.
- Derivation of the conjugate gradient method
- Conjugate residual method
- Hilbert–Schmidt expansion theorem
- L2 convergence of Fourier series
- Minimal residual method
- Wavelet
- Karhunen–Loève theorem
- Tensor product of Hilbert spaces
- Bilinear series of a symmetric kernel
- Lanczos algorithm
- Spectral theorem for compact self-adjoint operators
- Courant–Fischer characterization of characteristic values
- Generalized minimal residual method
- 3-j symbol
- Trace class operator
- Arnoldi iteration
- Nonlinear approximation
- Multiresolution analysis
- Lidskii's trace formula for integral operators
- Approximation of a kernel by degenerate kernels
- Spectrum of the Laplace–Beltrami operator
- Fourier series method
- Bergman kernel
- Biconjugate gradient stabilized method
- Compactness of integral operators
- Hilbert–Schmidt operator
- Addition theorem for spherical harmonics
- Fourier basis of L2 of the circle
- Jentzsch's theorem on positive kernels
- Haar system
- Mercer's theorem
- Principal component analysis
- Weyl–von Neumann theorem
- Walsh function
- Basel problem via Fourier series
- Singular values of a compact operator
- Riesz basis
- Schmidt's singular value decomposition of a kernel
Further reading
- Web https://en.wikipedia.org/wiki/Orthonormal_basis, lead section
About this page
| Tag | 0S9GGTR0EX |
|---|---|
| URI | m2://0S9GGTR0EX |
| Kind | concept |
| Writing | W1 stated |
| MSC | 15A63, 46C05 |
| Specializes | Basis, Orthonormal family |
| Same as |
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Definitions
Used by
- Wavelet
- Karhunen–Loève theorem
- Tensor product of Hilbert spaces
- Bilinear series of a symmetric kernel
- Lanczos algorithm
- Spectral theorem for compact self-adjoint operators
- 3-j symbol
- Trace class operator
- Nonlinear approximation
- Multiresolution analysis
- Approximation of a kernel by degenerate kernels
- Fourier series method
- Bergman kernel
- Hilbert–Schmidt operator
- Addition theorem for spherical harmonics
- Fourier basis of L2 of the circle
- Haar system
- Principal component analysis
- Weyl–von Neumann theorem
- Walsh function
- Riesz basis