Diclib.com
Словарь ChatGPT

Поиск в словаре Индивидуальные решения

Введите слово или словосочетание на любом языке 👆

Язык:

Перевод и анализ слов искусственным интеллектом ChatGPT

На этой странице Вы можете получить подробный анализ слова или словосочетания, произведенный с помощью лучшей на сегодняшний день технологии искусственного интеллекта:

как употребляется слово
частота употребления
используется оно чаще в устной или письменной речи
варианты перевода слова
примеры употребления (несколько фраз с переводом)
этимология

Что (кто) такое algebras - определение

VECTOR SPACE EQUIPPED WITH A BILINEAR PRODUCT

Algebra over a commutative ring; Unital algebra; Algebra (ring theory); Algebras; Algebra over a ring; K-algebra; Distributive algebra; Algebra (module); Comeasuring; Algebras over a field; An algebra; Algebra over the complex numbers

Найдено результатов: 591

algebras

Phone number (digits). From The Jamie Foxx Show.
That honey's cute. Slip her my algebras.

Algebra over a field

In mathematics, an algebra over a field (often simply called an algebra) is a vector space equipped with a bilinear product. Thus, an algebra is an algebraic structure consisting of a set together with operations of multiplication and addition and scalar multiplication by elements of a field and satisfying the axioms implied by "vector space" and "bilinear".

https://en.wikipedia.org/wiki/Algebra_over_a_field

Algebra homomorphism

RING HOMOMORPHISM PRESERVING SCALAR MULTIPLICATION

Algebra isomorphism; Homomorphism of algebras; Algebra endomorphism; Algebra automorphism

In mathematics, an algebra homomorphism is a homomorphism between two associative algebras. More precisely, if and are algebras over a field (or commutative ring) , it is a function F\colon A\to B such that for all in and in ,

https://en.wikipedia.org/wiki/Algebra_homomorphism

Sheaf of algebras

Affine morphism; Draft:Sheaf of algebras

In algebraic geometry, a sheaf of algebras on a ringed space X is a sheaf of commutative rings on X that is also a sheaf of \mathcal{O}_X-modules. It is quasi-coherent if it is so as a module.

https://en.wikipedia.org/wiki/Sheaf_of_algebras

Classification of Clifford algebras

Classification of clifford algebras; Pseudoscalar (Clifford algebra)

In abstract algebra, in particular in the theory of nondegenerate quadratic forms on vector spaces, the structures of finite-dimensional real and complex Clifford algebras for a nondegenerate quadratic form have been completely classified. In each case, the Clifford algebra is algebra isomorphic to a full matrix ring over R, C, or H (the quaternions), or to a direct sum of two copies of such an algebra, though not in a canonical way.

https://en.wikipedia.org/wiki/Classification_of_Clifford_algebras

Clifford algebra

ALGEBRAIC STRUCTURE GENERATED BY A VECTOR SPACE WITH A QUADRATIC FORM AND A UNITAL ASSOCIATIVE ALGEBRA STRUCTURE

Clifford algebras; Clifford group; Clifford Algebra; Clifford multiplication; Clifford relation; Clifford product; Clifford number; Cℓ; Clifford–Lipschitz group; Clifford-Lipschitz group; Lipschitz group

In mathematics, a Clifford algebra is an algebra generated by a vector space with a quadratic form, and is a unital associative algebra. As -algebras, they generalize the real numbers, complex numbers, quaternions and several other hypercomplex number systems.

https://en.wikipedia.org/wiki/Clifford_algebra

Boolean algebras canonically defined

A TECHNICAL TREATMENT OF BOOLEAN ALGEBRAS

Yet another perspective on Boolean algebras; Power set algebra

Boolean algebra is a mathematically rich branch of abstract algebra. Stanford Encyclopaedia of Philosophy defines Boolean algebra as 'the algebra of two-valued logic with only sentential connectives, or equivalently of algebras of sets under union and complementation.

https://en.wikipedia.org/wiki/Boolean_algebras_canonically_defined

Advances in Applied Clifford Algebras

JOURNAL

Advances in applied clifford algebras; Advances in Applied Clifford Algebra; Adv Appl Clifford Algebr; Adv. Appl. Clifford Algebr.; Adv Appl Clifford Algebras; Adv. Appl. Clifford Algebras

Advances in Applied Clifford Algebras is a peer-reviewed scientific journal that publishes original research papers and also notes, expository and survey articles, book reviews, reproduces abstracts and also reports on conferences and workshops in the area of Clifford algebras and their applications to other branches of mathematics and physics, and in certain cognate areas. There is a vibrant and interdisciplinary community around Clifford and Geometric Algebras with a wide range of applications.

https://en.wikipedia.org/wiki/Advances_in_Applied_Clifford_Algebras

Tensor product of algebras

TENSOR PRODUCT OF ALGEBRAS OVER A FIELD; ITSELF ANOTHER ALGEBRA

Tensor product of R-algebras; Tensor product of rings; Tensor product algebra

In mathematics, the tensor product of two algebras over a commutative ring R is also an R-algebra. This gives the tensor product of algebras.

https://en.wikipedia.org/wiki/Tensor_product_of_algebras

Schröder–Bernstein theorems for operator algebras

Schröder–Bernstein Theorem for von Neumann algebras; Schröder–Bernstein theorem for von Neumann algebras; Schroder-Bernstein Theorem for von Neumann algebras; Schroeder-Bernstein theorem for von Neumann algebras; Schroeder-Bernstein Theorem for von Neumann algebras; Schroder-Bernstein theorem for von Neumann algebras; Schroder-Bernstein theorems for operator algebras; Schroeder-Bernstein theorems for operator algebras; Schröder-Bernstein theorems for operator algebras; Schröder-Bernstein theorem for von Neumann algebras; Schröder-Bernstein Theorem for von Neumann algebras; Schroder–Bernstein theorems for operator algebras; Schröder–Bernstein theorem for operator algebras; Schröder-Bernstein theorem for operator algebras

The Schröder–Bernstein theorem from set theory has analogs in the context operator algebras. This article discusses such operator-algebraic results.

https://en.wikipedia.org/wiki/Schröder–Bernstein_theorems_for_operator_algebras

Википедия

Algebra over a field

In mathematics, an algebra over a field (often simply called an algebra) is a vector space equipped with a bilinear product. Thus, an algebra is an algebraic structure consisting of a set together with operations of multiplication and addition and scalar multiplication by elements of a field and satisfying the axioms implied by "vector space" and "bilinear".

The multiplication operation in an algebra may or may not be associative, leading to the notions of associative algebras and non-associative algebras. Given an integer n, the ring of real square matrices of order n is an example of an associative algebra over the field of real numbers under matrix addition and matrix multiplication since matrix multiplication is associative. Three-dimensional Euclidean space with multiplication given by the vector cross product is an example of a nonassociative algebra over the field of real numbers since the vector cross product is nonassociative, satisfying the Jacobi identity instead.

An algebra is unital or unitary if it has an identity element with respect to the multiplication. The ring of real square matrices of order n forms a unital algebra since the identity matrix of order n is the identity element with respect to matrix multiplication. It is an example of a unital associative algebra, a (unital) ring that is also a vector space.

Many authors use the term algebra to mean associative algebra, or unital associative algebra, or in some subjects such as algebraic geometry, unital associative commutative algebra.

Replacing the field of scalars by a commutative ring leads to the more general notion of an algebra over a ring. Algebras are not to be confused with vector spaces equipped with a bilinear form, like inner product spaces, as, for such a space, the result of a product is not in the space, but rather in the field of coefficients.

https://en.wikipedia.org/wiki/Algebra over a field