corresponding basis

USAGE SUMMARY

The phrase "corresponding basis" is correct and usable in written English.
It can be used in mathematical or scientific contexts to refer to a set of vectors or elements that correspond to a particular structure or system. Example: "In linear algebra, each vector can be expressed in terms of the corresponding basis of the vector space."

✓ Grammatically correct

Science

Academia

Wiki

Human-verified examples from authoritative sources

Exact Expressions

14 human-written examples

The Stuttgart small-core pseudopotentials and corresponding basis sets were used for the core valence interactions.

Acta Materialia

Since the corresponding basis is adapted to the composition of the signal, the transform can well reveal its characteristics.

Journal of Sound and Vibration

The first comprising the basis functions, and the second encoding the weights of the corresponding basis functions.

EURASIP Journal on Audio, Speech, and Music Processing

Let (mathsf {Y}={y_0, y_1, ldots, y_{d-1}}) be the corresponding basis of the right module (Phi _G).

Bulletin of Mathematical Sciences

The corresponding basis (mathsf {W}_infty ) of (C(X^omega, Bbbk )) is called the Walsh basis, see [51].

Bulletin of Mathematical Sciences

The corresponding basis functions ϕ j ∈ V h, j = 1, …, m, are defined by ϕ j ( p i ) = δ i j (Kronecker's symbol).

Boundary Value Problems

Human-verified similar examples from authoritative sources

Similar Expressions

46 human-written examples

We used the LANL2DZ effective core potentials and corresponding valence basis sets for the metals and 6-311+G* 6-311+G*tron basis sets for C, N, O, and H.

Cell Research

The corresponding derivative basis functions are used to calculate the derivative of the basis function with respect to the angular frequency (sinusoid) and decay rate (damping function).

Biotechnology for Biofuels

The final surface is defined by all the input control vertices with their corresponding mapped basis functions.

Computer Methods in Applied Mechanics and Engineering

The corresponding modal basis of the transmission simulator is described by the fixed-interface modes, rather than free modes that were used in the original approach.

Journal of Sound and Vibration

Numerical tests, conducted for the set of molecules show good agreement between dispersion coefficients, calculated with developed explicitly-correlated method and corresponding complete basis set results in regular CCSD already at triple-ζ level.

Chemical Physics Letters

Expert writing Tips

Best practice

When using the term "corresponding basis", ensure the relationship or correspondence is clearly defined within the context. Specify what the basis is corresponding to in order to avoid ambiguity.

Common error

Avoid using "corresponding basis" without specifying what the basis corresponds to. This can lead to confusion and misinterpretation. Always clarify the link between the basis and the element it relates to.

Linguistic Context

The phrase "corresponding basis" functions primarily as a noun phrase, often used in mathematical and scientific contexts to denote a basis that is related to another basis or a specific element within a system. As Ludwig AI highlights, it is used to indicate a clear relationship between sets of elements.

Expression frequency: Common

Frequent in

Science

75%

Academia

17%

Wiki

8%

Less common in

News & Media

0%

Formal & Business

0%

Encyclopedias

0%

Ludwig's WRAP-UP

In summary, "corresponding basis" is a grammatically correct and commonly used phrase, primarily within scientific and academic fields. It denotes a basis specifically related to another element or structure. As Ludwig AI confirms, the phrase is well-established in formal writing. When employing "corresponding basis", ensure you clearly define the relationship to avoid ambiguity. Alternatives include ""related basis"" or "associated basis", depending on the nuance you wish to convey. Remember that the phrase is most appropriate for formal, technical writing and should be avoided in informal contexts. By following these guidelines, you can use "corresponding basis" effectively and accurately in your writing.

More alternative expressions

Phrases that express similar concepts, ordered by semantic similarity:

related basis

Replaces "corresponding" with "related", emphasizing the connection between the bases.

associated basis

Substitutes "corresponding" with "associated", highlighting the link between the basis and a specific element or structure.

matching basis

Replaces "corresponding" with "matching", indicating a direct equivalence or alignment between the bases.

respective basis

Specifies that each element has its own individual basis.

equivalent basis

Indicates the basis is functionally the same as another basis, although perhaps represented differently.

analogous basis

Suggests the basis is similar to another basis in certain aspects, but not necessarily identical.

counterpart basis

Implies the existence of a basis that mirrors or complements another.

correlated basis

Highlights the statistical relationship between the basis and some other variable or structure.

interrelated basis

Focuses on the mutual connections and dependencies between the basis and other elements.

complementary basis

Indicates that the basis completes or enhances another basis.

FAQs

How is "corresponding basis" used in linear algebra?

In linear algebra, the "corresponding basis" refers to a set of vectors that form a basis for a vector space and are specifically related to another vector space or transformation. For instance, when mapping vectors between spaces, each vector in the original space has a "related basis" in the target space.

What are some alternatives to "corresponding basis" in a scientific context?

Depending on the specific context, alternatives to "corresponding basis" may include "associated basis", ""related basis"", or "matching basis". The best choice depends on the precise relationship you wish to convey.

How do I clarify the relationship when using "corresponding basis"?

To clarify the relationship, explicitly state what the basis is corresponding to. For example, "the corresponding basis of the dual space" or "the corresponding basis for the transformed vectors". This avoids ambiguity and ensures clear communication.

Is there a difference between "corresponding basis" and "equivalent basis"?

Yes, while similar, "corresponding basis" implies a specific relationship or mapping between two bases, whereas "equivalent basis" suggests that two bases are functionally interchangeable, potentially without a direct mapping between their elements. The choice depends on whether you want to emphasize a specific link or functional similarity.