Sentence examples for between two real vector from inspiring English sources

In fact, they proved that a mapping between two real vector spaces and is a solution of (1.5) if and only if there exists a unique symmetric multiadditive mapping such that for all.

In fact, they proved that a mapping between two real vector spaces and is a solution of (1.2) if and only if there exists a unique symmetric multi-additive mapping such that for all (see [7, 11]).

They proved that a mapping f between two real vector spaces X and Y is a solution of (1.3) if and only if there exists a unique mapping C : X × X × X → Y such that f (x) = C x, x, x) for all x ∈ X, moreover, C is symmetric for each fixed one variable and is additive for fixed two variables.

Jun and Kim proved that a mapping between two real vector spaces and is a solution of (1.1) if and only if there exists a unique mapping such that for all ; moreover, is symmetric for each fixed one variable and is additive for fixed two variables.

They proved that a mapping f between two real vector spaces X and Y is a solution of (1.2) if and only if there exists a unique mapping C : X × X × X → Y such that f ( x ) = C ( x, x, x ) for all x ∈ X.

In fact, they proved that a mapping f between two real vector spaces X and Y is a solution of (1 3) if and only if there exists a unique symmetric multi-additive mapping M : X4 → Y such that f(x) = M x, x, x, x) for all x.

Let be real numbers, and and be two real vectors, then if and only if.

Each dot product of two real vectors with length N has the flop count of 2N, whereas the flop count for two complex vectors is 8N.

Real causal relations are relations between two real things, however.

Warrington edge a fine encounter between two real contenders.

with a(t i ) and b(t i ) two real l-vectors.