orthogonal orthonormalize In context|mathematics|lang=en terms the difference between orthogonal and orthonormalize is thatorthogonalis (mathematics) whileorthonormalizeis (mathematics) to make a set of vectors both orthogonal and normalized. As a adjectiveorthogonal ...
As adjectives the difference between usual and normal is that usual is most commonly occurring while normal is...
4.2 Orthogonal/orthonormal DCT/DST matrices: definitions, properties and relations Before deriving the explicit forms of orthonormal DCT and DST matrices we recall their definitions, basic mathematical properties and relations. N is assumed to be an integer power of 2. A subscript in the matrix nota...
We analyze relations between the matrix coefficients of the three term relations for the orthonormal polynomials as well as the coefficients of the structure relations satisfied by these bivariate semiclassical orthogonal polynomials, also a matrix differential-difference equation for the bivariate orthogonal...
For tensors in Sym3, shape has three degrees of freedom (because the three eigenvalues are independent), and we intend to define at each tensor D an orthonormal basis for shape variation. Orthogonal Invariants. We build upon work by Ennis and Kindlmann that advocates sets of orthogonal ...
I and the eigenspace of eigenvalue 1 has dimension 1. • For any A ∈ L(V ) that is orthogonal to ˜ I (with respect to the Hilbert-Schmidt inner product, i.e. Tr(A ˜ I) = 0) it holds that E(A) 2 ≤λ A 2 . A quantum expander is explicit if E can be impleme...
three degrees of freedom (because the three eigenvalues are independent), and we intend to define at each tensor D an orthonormal basis for shape variation. Orthogonal Invariants. We build upon work by Ennis and Kindlmann that advocates sets of orthogonal invariants for DTI analysis [15]. In...
We analyze relations between the matrix coefficients of the three term relations for the orthonormal polynomials as well as the coefficients of the structure relations satisfied by these bivariate semiclassical orthogonal polynomials, also a matrix differential-difference equation for the bivariate orthogonal...
Then, EM field operators are expanded by the CL operators weighted by non-orthogonal and spatially-localized bases, which can be interpreted as propagators of initial quantum electromagnetic (complex-valued) field operators (QEM-CV-propagators); however, unlike the classical propagator [27,28] ...