Sentence examples for exists a basis from inspiring English sources

It remains a conjecture as to whether there always exists a basis of paths in which the blue is a convex combination.

Since E is a Hilbert space, then there exists a basis { v n } ⊂ X such that X = ⨁ j ≥ 1 X j ¯, where X j = span { v j }.

Equation (2.1) is disconjugate on a compact interval if and only if there exists a basis of solutions such that (2.2). on.

Then there exists a basis { e 1, e 2, …, e n } for X such that ∥ e i ∥ = 1 and e i ⊥ B [ { e k } k ≠ i ] for all i = 1, 2, …, n.

For a given time interval, say [0, T], regularly sampled with N samples, and a fixed bandwidth [-F, F], one can ensure that there exists a basis with d sequences of length N that concentrate most of their energy inside [-F, F], provided T ≥ d/(2F).

If ((mathbb{Y}, { p_{i} } _{iin I} )) is a locally convex space, then a convex cone (mathbb{K}subsetmathbb{Y}) is said to be normal if there exists a basis B of ({ p_{i} } _{iin I}) such that, for each (pin B) and all (x,yinmathbb{K}), thetapreceq xpreceq yquad Longrightarrowquad p (x )leqslant p (y ).

(HCP9 SMH) One of the key ways the SMH program built credibility and trust among the physicians of the host institution was by voluntarily limiting the scope of chiropractic practice to musculoskeletal complaints for which there existed a basis in scientific evidence.

Then there exists a orthonormal basis {e k } of H, and also is one orthogonal basis of H2.

Previous work in the latter area is surveyed, to determine whether there exists a suitable basis for the ISO 10303 work, and progress and technical problems are reviewed.

Then there exists a Hilbert basis composed of eigenvectors of (mathcal{T}).

The answer is Yes if and only if there exists a common basis in these two matroids.