Sentence examples for having basis from inspiring English sources

The path K -algebra of F (also known as the quiver K -algebra of F ), denoted K F, is the K -vector space having basis F 0 ⊔ F 1, with multiplication given by the K -linear extension of p · q = p q if r ( p ) = s ( q ) 0 otherwise.

Let V [ p ] denote the K -vector space having basis [ p ], consisting of the distinct elements of E ∞ which are tail-equivalent to p. For v ∈ E 0, e ∈ E 1, and q = f 1 f 2 f 3 ⋯ ∈ [ p ], define v · q = q if v = s ( f 1 ) 0 otherwise, e · q = e q if r ( e ) = s ( f 1 ) 0 otherwise, and e ∗ · q = τ > 1 ( q ) if e = f 1 0 otherwise.

For once screaming triumphalism had basis in an emphatic victory, by 17 points to 11.

His comments bothered me because they reminded me that my fears have basis.

Sometimes strange requests turn out having a basis in fact.

Litter was collected, dried and weighed, and expressed on a mass per ha basis.

That assumption had no basis in fact.

The accusations have no basis in fact".

It has no basis in the fundamentals.

"They have no basis here.

They have no basis in economics.