Sentence examples for be the linear span from inspiring English sources

Let (mathfrak {C}) be the linear span of all products (A_1B_1) for (A_1in mathfrak {A}), (B_1in mathfrak {B}).

Let (X_{B}) be the linear span of B, endowed with the topology generated by the Minkowski gauge of B, (rho _{B}).

Let (D_{min}^{prime}) be the linear span of (C^{infty}) functions with compact support in a single interval ((x_{i-1},x_{i})), (iinmathbb{N}).

Define W to be the linear span of the finite set begin{aligned} { tau e in L_mathbb {K}(E) :tau text { is a path ending in } v, ~ e in Y }. end{aligned}Notice that (dim (W) ge |Y| = N).

Let M + be the positive part of ℳ. Set S + ( M ) = { x ∈ M + : τ ( s ( x ) ) < ∞ } and let S ( M ) be the linear span of S + ( M ), we will often abbreviate S + ( M ) and S ( M ), respectively, as S + and.

Note that, in particular, (g_i|_{A_i}) and (h_j|_{B_j}) are injective, where (A_i) is the linear span of (L_i) and (B_j) is the linear span of (R_j).

where L Open image in new window is the linear span, and C l p is the closure in the topology of point convergence.

We denote by P n the orthogonal projector of L 2 onto M n which is the linear span of { w 1, w 2, …, w n }.

Hence, for any subset of there is the smallest subalgebra of containing This algebra is called the subalgebra of generated by If is the singleton then is the linear span of all powers of If is a normed algebra, the closed algebra generated by a set is the smallest closed subalgebra containing We can see that.

The Wick product of exponentials (varepsilon (f)) and (varepsilon (g)) is defined as ( varepsilon (f) lozenge varepsilon (g)=varepsilon (f+g),) where (mathcal {E}={sum ^{n}_{k=1}a_{k}varepsilon (f_{k}),) (nin mathbb {N}, a_{k}in R, f_{k}in R^{n}) for (k in {1,ldots,n}}) is the linear span of the exponentials.

Let be a connected open subset of, let be the standard unit basis of, and let be the linear space of -covectors, spanned by the exterior products, corresponding to all ordered -tuples,,.