Sentence examples for a linear subspace of from inspiring English sources

P is a linear subspace of ℓ∞.

Then W is a linear subspace of (R^{2}).

Let ℭ be a linear subspace of ℂ.

Moreover, A ( m ) is a linear subspace of S ( m ) for any m ∈ N ( 0 ).

(G(mathcal{T}^{-1})) is a linear subspace of (Ytimes X).

AP is a linear subspace of ℓ∞ and P ⊂ P ̄ = S P ⊂ A P ⊂ ℓ ∞.

For a linear subspace A of ({mathcal A}), set begin{aligned} mu (A) = lim _{omega } frac{dim (Acap W_i)}{dim (W_i)}.

A linear subspace S of an algebra G is called reflexive if a ∈ S whenever a ∈ G and paq = 0 for every pair p, q of indempotents in G such that pSq = {0}.

For each (k in mathbb {N}_0), define a linear subspace (W_k) of (L_mathbb {K}(E)) by begin{aligned} W_k = mathrm {span}( { gamma mu _0^k :gamma in mathcal {P} } ) end{aligned}Thus for any different (k,l in mathbb {N}_0), we have (dim (W_k) = |mathcal {P}|) and the collection of subspaces ({ W_k }) is independent.

Of special importance is the notion of a closed linear subspace of a Hilbert space that, with the inner product induced by restriction, is also complete (being a closed set in a complete metric space) and therefore a Hilbert space in its own right.

MPCA computes a linear subspace representing the variance of data due to the variation of each factor as well as the linear subspace of the image space itself.