orthonormal

Adjective

Meaning

(mathematics) Of a set of vectors, both orthogonal and normalized.

(mathematics) Of a linear transformation that preserves both angles and lengths.

Related terms

Examples

An orthonormal sequence in a Hilbert space is a simple example of a weakly convergent sequence, with limit equal to the 0 vector. Source: Internet

Complete orthonormal systems of wave functions appear naturally as the eigenfunctions of the Hamiltonian (of a bound system ) in quantum mechanics that measures the energy levels, which are called the eigenvalues. Source: Internet

For simplicity, we assume that they are discrete, and that they are orthonormal, i.e., : Note that these basis states are assumed to be independent of time. Source: Internet

Any complete inner product space V has an orthonormal basis. Source: Internet

An orthonormal basis is a basis where all basis vectors have length 1 and are orthogonal to each other. Source: Internet

In most cases of practical interest, the orthonormal basis comes from an integral or differential operator, in which case the series converges in the distribution sense. Source: Internet

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