Examples of 'non-commutative' in a sentence
Meaning of "non-commutative"
Non-commutative (adjective): Refers to a mathematical property where the order of operation affects the outcome, such as in matrix multiplication. It is the opposite of commutative operations like addition or multiplication
How to use "non-commutative" in a sentence
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non-commutative
In general operator algebras are non-commutative rings.
The non-commutative case is discussed in detail in the respective articles.
My primary research area is non-commutative algebra.
However, a non-commutative cancellative monoid need not be embeddable in a group.
Dimensional regularization and non-commutative geometry.
An example of a non-commutative ring is the ring of square matrices of the same size.
It relies on the difficulty of factoring in a non-commutative polynomial ring.
In the non-commutative ring case the same definition does not always work.
Or you have had to work with non-commutative algebras.
The variables must be non-commutative otherwise the second polynomial would be identically zero.
The order of rotations is important, because a rotation is a non-commutative operation.
A geometry with a non-commutative multiplication.
Such results show that transformation geometry includes non-commutative processes.
Then he became interested in non-commutative martingales and stochastic calculus.
Representation theory is a branch of mathematics that draws heavily on non-commutative rings.
See also
One example of this is the use of non-commutative algebra to study geometry.
For example, matrix multiplication and quaternion multiplication are both non-commutative.
After that, he concentrated on non-commutative ring theory and the theory of algebras.
Yet another application concerns the three-dimensional non-commutative oscillator.
In mathematics, quaternions are a non-commutative number system that extends the complex numbers.
Definition and simple examples of modules over commutative and non-commutative rings.
Some of the most popular versions for non-commutative spaces explicitly violate lorentz invariance.
But in the study of the algebras of operators one often encounters non-commutative properties.
He is a world expert on non-commutative algebra and geometry, and has steered this subject forward.
We give applications of this results to the formulas of non-commutative cluster mutations.
Public and non-commutative proxy encryption schemes provide a key mechanism for implementing a wide range of applications.
One can use this isomorphism to construct a lot of non-commutative endomorphism rings.
The non-commutative Iwasawa theory of modular forms.
Today, studies are being done on the relationship between non-commutative probability and topological data analysis.
As will be shown below, the Mambo and Okamoto schemes are private and non-commutative.
This concept is generalized to non-commutative rings in the Semiprime ring article.
These theories can not be obtained simply by writing usual field theory on non-commutative spaces.
Zhang algebras are non-commutative analogues of groups and contain the class of Voiculescu 's dual groups.
In that subject, one has the subareas of commutative ring theory and non-commutative ring theory.
Non-commutative geometry and the Standard Model with neutrino mixing.
This protocol describes how to encrypt a secret message and then decrypt using a non-commutative group.
Therefore, the quaternions H are a non-commutative associative algebra over the real numbers.
The Chinese remainder theorem does not hold in the non-commutative case.
Quantum ergodicity can be formulated as a non-commutative analogue of the classical ergodicity T. Sunada.
The most systematic expression of this reevaluation is Alain Connes ' non-commutative geometry.
Problems in non-commutative algebra can be tackled with the Singular offspring Plural.
The decomposition does not hold in general for non-commutative Noetherian rings.
This is a non-commutative simple ring.
In the last ten years Coates studied some aspects of non-commutative Iwasawa theory.
They are a non-commutative algebra.
Notably, the matrix exponentials are non-commutative.
Non-commutative harmonic analysis.
String concatenation is an associative, but non-commutative operation.
Non-commutative differentiable manifold.
It states that dualization and discretization are, in general, non-commutative operations.
