* In the spectral decomposition of matrices, lambda indicates the diagonal matrix of the eigenvalues of the matrix ( mathematics ).

* Cylindrical algebraic decomposition, in mathematics

In mathematics, factorization ( also factorisation in British English ) or factoring is the decomposition of an object ( for example, a number, a polynomial, or a matrix ) into a product of other objects, or factors, which when multiplied together give the original.

In mathematics, a Voronoi diagram is a special kind of decomposition of a metric space, determined by distances to a specified family of objects ( subsets ) in the space.

In mathematics, Jordan decomposition may refer to

In physics and mathematics, in the area of vector calculus, Helmholtz's theorem, also known as the fundamental theorem of vector calculus, states that any sufficiently smooth, rapidly decaying vector field in three dimensions can be resolved into the sum of an irrotational ( curl-free ) vector field and a solenoidal ( divergence-free ) vector field ; this is known as the Helmholtz decomposition.

In mathematics, a handle decomposition of an m-manifold M is a union

In mathematics, the Bruhat decomposition ( named after François Bruhat ) G = BWB into cells can be regarded as a general expression of the principle of Gauss – Jordan elimination, which generically writes a matrix as a product of an upper triangular and lower triangular matrices — but with exceptional cases.

In mathematics, the Iwasawa decomposition KAN of a semisimple Lie group generalises the way a square real matrix can be written as a product of an orthogonal matrix and an upper triangular matrix ( a consequence of Gram-Schmidt orthogonalization ).

In mathematics, a graded vector space is a type of vector space that includes the extra structure of gradation, which is a decomposition of the vector space into a direct sum of vector subspaces.

* Prime decomposition of integers, see fundamental theorem of arithmetic ( for the mathematics ) or integer factorization ( for applications )

In mathematics, particularly in linear algebra and functional analysis, the polar decomposition of a matrix or linear operator is a factorization analogous to the polar form of a nonzero complex number z as

In mathematics, the term cycle decomposition can mean:

Multipole moments in mathematics and mathematical physics form an orthogonal basis for the decomposition of a function, based on the response of a field to point sources that are brought infinitely close to each other.

* Levi decomposition in mathematics ( including Levi theorem, Levi subgroup, Levi subalgebra )

It should be stressed that the kinematical decomposition we are about to describe is pure mathematics valid for any Lorentzian manifold.

In mathematics, composition operators commonly occur in the study of shift operators, for example, in the Beurling-Lax theorem and the Wold decomposition.

In mathematics, Shannon's expansion or the Shannon decomposition is a method by which a Boolean function can be represented by the sum of two sub-functions of the original.

Blind students also complete mathematical assignments using a braille-writer and Nemeth code ( a type of braille code for mathematics ) but large multiplication and long division problems can be long and difficult.

The axiom of choice has also been thoroughly studied in the context of constructive mathematics, where non-classical logic is employed.

Although the axiom of countable choice in particular is commonly used in constructive mathematics, its use has also been questioned.

It is also commonly used in mathematics in algebraic solutions representing quantities such as angles.

The term may be also used loosely or metaphorically to denote highly skilled people in any non -" art " activities, as well — law, medicine, mechanics, or mathematics, for example.

He also applied mathematics in generalizing physical laws from these experimental results.

Despite being quite religious, he was also interested in mathematics and science, and sometimes is claimed to have contradicted the teachings of the Church in favour of scientific theories.

He was educated at the Collège des Quatre-Nations ( also known as Collège Mazarin ) from 1754 to 1761, studying chemistry, botany, astronomy, and mathematics.

His criticisms of the scientific community, and especially of several mathematics circles, are also contained in a letter, written in 1988, in which he states the reasons for his refusal of the Crafoord Prize.

He is also noted for his mastery of abstract approaches to mathematics and his perfectionism in matters of formulation and presentation.

In mathematics, the axiom of regularity ( also known as the axiom of foundation ) is one of the axioms of Zermelo – Fraenkel set theory and was introduced by.

It can also be used in topics as diverse as mathematics, gastronomy, fashion and website design.

In classical mathematics, analytic geometry, also known as coordinate geometry, or Cartesian geometry, is the study of geometry using a coordinate system and the principles of algebra and analysis.

He won a scholarship to the University and majored in mathematics, and also studied astronomy, physics and chemistry.

His father, Étienne Pascal ( 1588 – 1651 ), who also had an interest in science and mathematics, was a local judge and member of the " Noblesse de Robe ".

In chemistry, physics, and mathematics, the Boltzmann distribution ( also called the Gibbs Distribution ) is a certain distribution function or probability measure for the distribution of the states of a system.

Bioinformatics also deals with algorithms, databases and information systems, web technologies, artificial intelligence and soft computing, information and computation theory, structural biology, software engineering, data mining, image processing, modeling and simulation, discrete mathematics, control and system theory, circuit theory, and statistics.

It can also be used to denote abstract vectors and linear functionals in mathematics.

In mathematics, especially functional analysis, a Banach algebra, named after Stefan Banach, is an associative algebra A over the real or complex numbers which at the same time is also a Banach space.

The term can also be applied to some degree to functions in mathematics, referring to the anatomy of curves.

Combinatorial problems arise in many areas of pure mathematics, notably in algebra, probability theory, topology, and geometry, and combinatorics also has many applications in optimization, computer science, ergodic theory and statistical physics.

It has also given rise to a new theory of the philosophy of mathematics, and many theories of artificial intelligence, persuasion and coercion.

Most undergraduate programs emphasize mathematics and physics as well as chemistry, partly because chemistry is also known as " the central science ", thus chemists ought to have a well-rounded knowledge about science.

Category theory is an area of study in mathematics that examines in an abstract way the properties of particular mathematical concepts, by formalising them as collections of objects and arrows ( also called morphisms, although this term also has a specific, non category-theoretical meaning ), where these collections satisfy some basic conditions.