orthonormal's Usage Examples:

This definition of orthonormal basis generalizes to.

, Vn of V yield an orthonormal basis of Kn (with respect to the standard.

Usually the sequence is required to be orthonormal, namely, ⟨ P n , P n ⟩ 1 , {\displaystyle \langle P_{n},P_{n}\rangle.

} Let φn denote the associated eigenfunctions, normalized to be orthonormal in L2(U).

By self-similarity, there are scaled versions W_k of W_0 and by completeness one hasL^2(\R)\mbox{closure of }\bigoplus_{k\in\Z}W_k,thus the set\{\psi_{k,n}(x)\sqrt2^{-k}\psi(2^{-k}x-n):\;k,n\in\Z\}is a countable complete orthonormal wavelet basis in L^2(\R).

(an orthonormal basis), but not necessarily as an infinite sum of the monomials xn.

In particular, orthogonal transformations map orthonormal bases to orthonormal bases.

An orthonormal function system (ONS) is an orthonormal basis in a vector space of functions.

For example, infinite orthonormal sequences converge weakly to zero, as demonstrated below.

An orthonormal frame for Ex is an ordered orthonormal basis for Ex, or, equivalently, a linear.

A set of vectors form an orthonormal set if all vectors.

wavelet series is a representation of a square-integrable (real- or complex-valued) function by a certain orthonormal series generated by a wavelet.