Sentence examples for a subspace of v from inspiring English sources

Around the point γ , where θ is the phase, we establish an orthonormal basis in a subspace of ( v, u, b ).

(15) We can check that (operatorname{Fix} varSigma)) is a subspace of V; furthermore (dimoperatorname{Fix} varSigma) = 1) because it can be described as the span of a single vector.

If dim V = n < ∞ and (V, ν, τ, τ*) is a PN space that is also a TV space and A is a subspace of V, then: (a) V is normable.

A nonempty subset W of a vector space V that is closed under addition and scalar multiplication (and therefore contains the 0-vector of V) is called a subspace of V. Subspaces of V are vector spaces (over the same field) in their own right.

Theorem 2 Let F be a -fuzzy subfield of a field F, let V be a linear space over F, and let V be a fuzzy subset of V. V is a -fuzzy linear subspace of V over F if and only if, for all x, y ∈ V, k, l ∈ F, we have (1) V ( k x + l y ) ∨ λ ≥ F ( k ) ∧ V ( x ) ∧ F ( l ) ∧ V ( y ) ∧ μ ;   (2) F ( 1 ) ∨ λ ≥ V ( x ) ∧ μ.  .

Definition 2 Let F be a -fuzzy subfield of a field F, V be a linear space over F and V be a fuzzy subset of V. V is called a -fuzzy linear subspace of V over F if for all x, y ∈ V, k ∈ F, we have (1) V ( x + y ) ∨ λ ≥ V ( x ) ∧ V ( y ) ∧ μ ;   (2) V ( − x ) ∨ λ ≥ V ( x ) ∧ μ ;   (3) V ( k x ) ∨ λ ≥ F ( k ) ∧ V ( x ) ∧ μ ;   (4) F ( 1 ) ∨ λ ≥ V ( x ) ∧ μ.  .

Thus f ( V 1 ) is a -fuzzy linear subspace of V 2 over F. □.

So, f − 1 ( V 2 ) is a -fuzzy linear subspace of V 1 over F. □.

The closure of a subspace can be completely characterized in terms of the orthogonal complement: If V is a subspace of H, then the closure of V is equal to V^{\bot\bot}.

We determine that a subspace W of V is simultaneously isotropic if W is isotropic with respect to all Q1,…,Q m.

It is well known (cf.  [63, p. 32]) that V al i ±, ∞ is a dense GL (n ) invariant subspace of V al i ±.