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- Antisymmetric contraction test for an antisymmetric tensor
- Antiunitary operator
- Best N-term approximation
- Brownian covariance from an integrated orthonormal basis
- Cameron-Martin space of a Gaussian measure
- Cartesian second-rank tensor
- Compression of a linear operator
- Diagonal absolute-sum bound for the trace norm
- Dirichlet realization of an elliptic operator
- Finite-Green-energy measure pairing with a Gaussian free field
- Fourier sine basis
- Fourier-Walsh transform
- Gelfand–Tsetlin basis of the standard representation
- Geodesic Hessian formula
- Green-kernel expansion in the Dirichlet space
- Haar scaling function
- Hecke operators are self-adjoint for the Petersson inner product
- Hilbert-Schmidt norm
- Hilbert-Schmidt operator
- Holonomy around circular fibres
- Interval-adapted wavelet basis
- Linear isometry of Hilbert spaces
- Matrix coefficient
- Maximally mixed state
- Measurement channel
- N-term approximation
- Orbital-frame rotation from inclination and node
- Orthogonal basis
- Orthogonal diagonalization of a real symmetric matrix
- Orthonormal eigenbasis
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- Quantum superposition
- Quotient theorem for Cartesian tensors
- Ramp-state expansion in a symmetric infinite well
- Rank-one dephasing
- Restricted likelihood from orthogonal error contrasts
- Scalar contraction test for a Cartesian tensor
- Scaling function
- Scaling refinement equation
- Spectral characterization of elliptic Dirichlet domains
- Spectral theorem for real symmetric matrices
- Tensor-power reduction of PBR overlap
- Thermal covariance of an elastic filament
- Unitary extension of a finite-dimensional isometry
- Wavefunction normalization
- Wavelet completion of a multiresolution filter
- Weak sequential compactness in a Hilbert space
- White-noise likelihood for a square-integrable shift
- Young orthogonal form
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An orthonormal basis is a specific type of basis used in linear algebra and functional analysis that has two key properties: orthogonality and normalization. 1. **Orthogonality**: Vectors in the basis are orthogonal to each other. Two vectors \( \mathbf{u} \) and \( \mathbf{v} \) are said to be orthogonal if their dot product is zero, i.e.