bijective mapping

USAGE SUMMARY

The phrase "bijective mapping" is correct and usable in written English. You can use it in mathematical contexts, particularly in discussions about functions and relations. For example, "A bijective mapping ensures that every element in the domain corresponds to a unique element in the codomain." Alternative expressions include "bijective function" and "one-to-one correspondence."

✓ Grammatically correct

Science

Academia

Encyclopedias

Human-verified examples from authoritative sources

Exact Expressions

46 human-written examples

The bijective mapping is achieved by minimizing a Dirichlet energy functional.

Computer Methods in Applied Mechanics and Engineering

We show that there is a bijective mapping between the proposed state-space representation and the augmented state-space.

Journal of Petroleum Science and Engineering

Also, it turns out that the proposed method is more effective to achieve the bijective mapping, especially near a concave boundary.

Computer Methods in Applied Mechanics and Engineering

The important properties of domain parameterization such as bijective mapping between parametric and physical domains, uniform mesh, and orthogonal mesh are enforced simultaneously.

Computer Methods in Applied Mechanics and Engineering

We say that two G-designs (Vi,Bi), i= 1,2, are exactly embedded into (X,D) if X= V1∪V2, |V1∩V2|="0 and there is a bijective mapping f:B1∪B2→D such that B is a subgraph of f(B), for every B∈B1∪B2.

Discrete Mathematics

From a technical point of view, we prove, among other things, that the set of theorems of the most common modal logics can be embedded (under the obvious bijective mapping between a modal and a first-order language) into that of the corresponding ML systems.

Artificial Intelligence

Human-verified similar examples from authoritative sources

Similar Expressions

14 human-written examples

For each pair of patches of the AIS subject and the control, we compute a bijective map using the holomorphic 1-form and harmonic map techniques.

Graphical Models

The aim of this paper is to provide a new approach to describe the general form of the transition probability preserving (not necessarily bijective) maps between Grassmann spaces.

Journal of Functional Analysis

The algorithm uses Newton method to invert a bijective map of the mesh elements onto a reference element, together with a criterion to move from element to element in the mesh.

Journal of Computational Physics

In 2001, Molnár provided a natural generalisation, namely, he provided a characterisation of (not necessarily bijective) maps which act on the Grassmann space of all rank-n projections and leave the system of Jordan principal angles invariant (see [17] and [20]).

Journal of Functional Analysis

It is shown that a bijective map ϕ:S(H →S(H) satisfies ϕ([ρ1,ρ2])⊆[ϕ ρ1),ϕ ρ2)] for any ρ1,ρ2∈S if and only if ϕ has one of the following formsρ↦MρM⁎tr(MρM⁎ orρ↦MρTM⁎tr(MρTM⁎), where M is an invertible bounded linear operator and ρT is the transpose of ρ with respect to an arbitrarily fixed orthonormal basis.

Journal of Functional Analysis

Expert writing Tips

Best practice

Ensure that the domain and codomain are clearly defined before applying this term to avoid ambiguity.

Common error

Do not use "bijective mapping" if you only intend to say that each input has a unique output. That is an "injective mapping". A "bijective mapping" requires that every element in the target set is also mapped from the source set.

Linguistic Context

As a noun phrase, "bijective mapping" serves as a precise technical term. It identifies a mathematical structure where elements of two sets are paired exactly. According to Ludwig, it often functions as the subject or the direct object in sentences describing isomorphisms or data transformations.

Expression frequency: Common

Frequent in

Science

75%

Academia

20%

Encyclopedias

5%

Less common in

News & Media

1%

Social Media

1%

Wiki

3%

Ludwig's WRAP-UP

In conclusion, "bijective mapping" is a cornerstone term for formal technical and mathematical communication. As demonstrated by the extensive examples in Ludwig, the phrase is indispensable for describing relationships that are both one-to-one and onto. Whether used in the context of state-space representations, genetic coding or metric spaces, it signifies a perfect, reversible pairing between two sets. Writers should favor this term when exactitude is required, though they should be mindful of its high formality level, which makes it most suitable for scholarly audiences.

More alternative expressions

Phrases that express similar concepts, ordered by semantic similarity:

one-to-one correspondence

Standard mathematical synonym that emphasizes the reciprocal relationship between two sets.

bijective function

Refers specifically to the function that performs the mapping.

bijection

The concise noun form used to identify the mapping itself.

one-to-one and onto mapping

Provides a descriptive breakdown of the two properties that define the phrase.

invertible mapping

Highlights the consequence of being bijective, which is that the map can be reversed.

isomorphism

A more specialized term in abstract algebra that implies a bijective mapping preserving structural properties.

bijective transformation

Commonly used in geometry or signal processing contexts.

reversible map

A more intuitive and slightly less formal way to describe the bidirectional nature of the mapping.

mutually unique mapping

An explanatory alternative that stresses the uniqueness of the pairing on both sides.

permutation

A specific type of bijective mapping where a set is mapped onto itself.

FAQs

How do I use "bijective mapping" in a sentence?

You can use it to describe a relationship between data sets, such as: "There is a "bijective mapping" between the proposed state-space representation and the augmented state-space."

What can I say instead of "bijective mapping"?

Depending on your context, you can use terms like ""one-to-one correspondence"", "bijective function" or simply "bijection".

What is the difference between a "bijective mapping" and an injective mapping?

While an injective mapping ensures every input has a unique output, a "bijective mapping" additionally requires that every possible output is mapped to by exactly one input.

Is "bijective mapping" formal enough for academic papers?

Yes, it is the standard formal term used in mathematics, computer science and physics. Ludwig AI shows it is extremely common in publications like ScienceDirect and Springer.