complete orthonormal set

complete orthonormal set

[kəm′plēt ¦ȯr·thō¦nȯr·məl ′set]
(mathematics)
A set of mutually orthogonal unit vectors in a (possibly infinite dimensional) vector space which is contained in no larger such set, that is no nonzero vector is perpendicular to all the vectors in the set. Also known as closed orthonormal set.
References in periodicals archive ?
where [e.sub.n](x) = [square root of (2/[pi])] sin(nx) is a complete orthonormal set of eigenvectors of A.Then, the following properties hold:
This ensures that the orbitals form a complete orthonormal set, so that other quantities can be expanded in this basis.
Likewise, the so-called natural orbitals [16] that diagonalize the one-particle reduced density matrix and thereby enable its most efficient representation cannot be employed; although the natural orbitals constitute a complete orthonormal set, they do not, in general, correspond to the eigenfunctions of a single-particle Hamiltonian with known eigenvalues, and for a collinear magnetic system they are also spin dependent.
(iii) There exists a complete orthonormal set [{[[PHI].sub.i]}.sup.[infinity].sub.i=1], of eigenvectors of A, such that
Later in this section (see Theorem 4.10), we prove that [E.sub.n] is, in fact, a complete orthonormal set in [H.sub.n] for each n [member of] N.
Since the set E = {[e.sub.m] | m [member of] [N.sub.0]} of eigenfunctions of A is a complete orthonormal set in [L.sup.2] [a, b], we see that
As remarked in Section 3, E is a complete orthonormal set in [L.sup.2] [a, b]; consequently, (4.19) implies that f = 0 in [L.sup.2] [a, b].
Guseinov, "New complete orthonormal sets of exponential-type orbitals in standard convention and their origin," Bulletin of the Chemical Society of Japan, vol.
Guseinov, "One-range addition theorems for noninteger n slater functions using complete orthonormal sets of exponential type orbitals in standard convention," Few-Body Systems, vol.
Guseinov, "Unified treatment of one-range addition theorems for complete orthonormal sets of generalized exponentialtype orbitals and noninteger N slater functions," Bulletin of the Chemical Society of Japan, vol.
By considering this deficiency, Guseinov had suggested a new centrally symmetric potential of the SF field and on the basis of this idea Guseinov proposed the new complete orthonormal sets of [[psi].sup.([alpha])]-ETOs.
To obtain the expansion of NISTO's about a new center by the use of complete orthonormal sets of [[PSI].sup.([alpha])]-ETOs we can use the method for the expansion of ISTOs.

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