Sentence examples for a standard basis from inspiring English sources

Suggestions(1)

The phrase "a standard basis" is correct and usable in written English.
It is typically used in mathematical contexts, particularly in linear algebra, to refer to a set of vectors that can be used to represent any vector in a given vector space.
Example: "In linear algebra, the standard basis for R^n consists of n vectors, each having a 1 in one coordinate and 0 in all others."
Alternatives: "a typical basis" or "a conventional basis".

Exact(11)

The values of the characteristics can form a standard basis for designing construction earthworks.

2.2.1, let ({ H_{sj} }) be a standard basis of (mathfrak {h}) and ({ vartheta _{sj} }) the corresponding dual basis.

Finally, a standard basis is generated which is completely equal with the original system, and which neither increases, nor decreases, the roots.

Then a standard basis vector is an eigenvector of the Jacobian matrix of the conjugate map at the fixed point, with associated eigenvalue 1.

The current paper presents a new AB2 algorithm based on the MSB-first scheme using a standard basis representation of Galois fields, GF 2m).

We show an algorithm with optimal competitive ratio 1/2 for the model where each bin in B is a standard basis vector.

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Via the new chemotaxis mechanism, each bacterium randomly selects a standard-basis-vector direction for swimming or tumbling; this approach may obviate calculating a random unit vector and could effectively get rid of interfering with each other between different dimensions.

It is a method of establishing the standard basis of a nonlinear polynomial system as follows.

A World Health Organization study meta-analysed 25 datasets identified by researchers attending a 1990 conference but lacked the literature search that is the standard basis of a systematic review.

For example, the coordinate vectors,, to, form a basis of, called the standard basis, since any vector can be uniquely expressed as a linear combination of these vectors:.

The l-form (u(x)=Sigma_{I}{u_{I}(x)}, dx_{I}) is a linear combination of the standard basis (dx^{I}=dx_{i_{1}}wedgecdotswedge dx_{i_{l}}) for all ordered l-tuples I.

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