Sentence examples for complement space from inspiring English sources

Specially, on H-type group G, there is a relation between the dimension of the center and its orthogonal complement space.

Take (X_{1}=operatorname{Ker}M) and let (X_{2}) be the complement space of (X_{1}) in X, so that, (X =X_{1} oplus X_{2}).

As the part in the complement space is no longer excited, it will follow the evolution as described in (32) and dies out.

where ξ ( x ip ) : = I m − x ip x ip H is the orthogonal projection operator onto the complement space of x ip.

Let X ˆ = Ker M and X ˜ be the complement space of X ˆ in X, then X = X ˆ ⊕ X ˜.

Suppose (Z_{1}) is a subspace of Z and (Z_{2}) is the complement space of (Z_{1}) in Z such that (Z=Z_{1}oplus Z_{2}).

It consists of a sensor head, electronics box, and GPS antenna, and was designed to complement space-borne magnetic measurements of the THEMIS mission, launched in 2007, with ground-based vector measurements of the geomagnetic field at 2 Hz cadence.

By defining the complement spaces via Galerkin projections, the related system of linear equations decouples and can be solved by standard multilevel finite element solvers.

However, l2-Sl0 is an unconstrained minimization problem which is to be solved in this paper by using three methods, namely quasi-Newton approach, conjugate gradient approach, and optimization in the null and complement spaces of the measurement matrix.

The new approach uses a smoothed l0-norm-regularized least squares (l2-Sl0) objective function and solves the optimization problem by three reconstruction algorithms: quasi-Newton, conjugate gradient (CG), and optimization in the null and complement spaces of measurement matrix (ONCS).

Three methods, namely quasi-Newton, conjugate gradient, and optimization in the null and complement spaces of the measurement matrix, are then proposed to solve the l2-Sl0 uncoptimizationproblemtion problem.