orthonormal


Also found in: Wikipedia.

orthonormal

(ˌɔːθəʊˈnɔːməl)
adj
orthogonal with the integral of the square of each function over a specified interval equal to one
Collins English Dictionary – Complete and Unabridged, 12th Edition 2014 © HarperCollins Publishers 1991, 1994, 1998, 2000, 2003, 2006, 2007, 2009, 2011, 2014
Translations
orthonormalorthonormé
References in periodicals archive ?
A direct verification shows that the system {[e.sub.z,[sigma]] | z [member of] Z, [sigma] [member of] [GAMMA]} is orthonormal in [L.sup.2]([0, 2[pi]], H), where [e.sub.z,[sigma]]s : [0, 2[pi]] [right arrow] H is defined by
Denote by K([pi]) or K(U [and] V) the sectional curvature of M associated with a plane section [pi] [subset.bar] [T.sub.p]M, where {U, V} is an orthonormal basis of [pi].
Let [{[[mu].sub.j]}.sup.[infinity].sub.j=1] be a sequence of its eigenvalues and [{[e.sub.j]}[infinity].sub.j=1] be an orthonormal basis of corresponding eigenvectors.
Guseinov, "New complete orthonormal sets of exponential-type orbitals in standard convention and their origin," Bulletin of the Chemical Society of Japan, vol.
where [V.sub.G] [member of] [R.sup.KxK] is orthonormal and [[SIGMA].sub.G] [member of] [R.sup.NxN] is the diagonal singular value matrix with all its elements being nonnegative, the incoherent dictionary can be obtained as
The topics include the nonlinear vibration control of three-dimensional irregular structures subjected to seismic loads, analyzing spatial variability in soil using geostatistics, adaptive fuzzy modeling using orthonormal basis functions to control the flow of network traffic, molecular dynamic simulations of the oxidative aging of asphalt molecules under stress and moisture, and applying cluster analysis in computational paleography.
A frame field {[u.sub.1], ..., [u.sub.n], ..., [u.sub.2n], [u.sub.2n+1]} in [E.sup.2n+1.sub.v] is called a pseudo orthonormal frame field, [9], if
We also produce a set of orthonormal basis functions for space solutions by using the kernel function, a boundary operator, a dense sequence of nodal points in the domain of space solution, and Gram-Schmidt orthogonalization process.
Putting X = Y = [e.sub.i] in (3.2) where {[e.sub.1], [e.sub.2], [e.sub.3],..., [e.sub.2n], [e.sub.2n+1] = [xi]} is an orthonormal basis of the tangent space at each point of the manifold M and taking the summation over i, 1 [less than or equal to] i [less than or equal to] 2n + 1, we get
This technique represents the random response of a model in terms of a linear combination of orthonormal polynomial basis involving the input random variables.
Therefore, [mathematical expression not reproducible] is an orthonormal frame of the normal bundle ([gamma](t)).sup.[perpendicular to]] along the spherical regular curve [gamma](t).