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General linear group and Orthogonal group

Shortcuts: Differences, Similarities, Jaccard Similarity Coefficient, References.

Difference between General linear group and Orthogonal group

General linear group vs. Orthogonal group

In mathematics, the general linear group of degree n is the set of invertible matrices, together with the operation of ordinary matrix multiplication. In mathematics, the orthogonal group in dimension, denoted, is the group of distance-preserving transformations of a Euclidean space of dimension that preserve a fixed point, where the group operation is given by composing transformations.

Similarities between General linear group and Orthogonal group

General linear group and Orthogonal group have 42 things in common (in Unionpedia): Algebraic variety, Bott periodicity theorem, Center (group theory), Characteristic (algebra), Commutator, Commutator subgroup, Compact space, Complex number, Connected space, Determinant, Dimension (vector space), Direct limit, Field (mathematics), Field with one element, Finite field, Fundamental group, Group (mathematics), Group action, Identity component, Identity matrix, Integer, Invertible matrix, Lie algebra, Lie group, Linear map, List of finite simple groups, Mathematics, Matrix multiplication, Multiplicative group, Normal subgroup, ..., Orientation (vector space), Orthogonal group, Quadratic form, Quotient group, Real number, Semidirect product, Simply connected space, Subgroup, Symmetric group, Symplectic group, Unitary group, Vector space. Expand index (12 more) »

Algebraic variety

Algebraic varieties are the central objects of study in algebraic geometry.

Algebraic variety and General linear group · Algebraic variety and Orthogonal group · See more »

Bott periodicity theorem

In mathematics, the Bott periodicity theorem describes a periodicity in the homotopy groups of classical groups, discovered by, which proved to be of foundational significance for much further research, in particular in K-theory of stable complex vector bundles, as well as the stable homotopy groups of spheres.

Bott periodicity theorem and General linear group · Bott periodicity theorem and Orthogonal group · See more »

Center (group theory)

In abstract algebra, the center of a group,, is the set of elements that commute with every element of.

Center (group theory) and General linear group · Center (group theory) and Orthogonal group · See more »

Characteristic (algebra)

In mathematics, the characteristic of a ring R, often denoted char(R), is defined to be the smallest number of times one must use the ring's multiplicative identity (1) in a sum to get the additive identity (0) if the sum does indeed eventually attain 0.

Characteristic (algebra) and General linear group · Characteristic (algebra) and Orthogonal group · See more »

Commutator

In mathematics, the commutator gives an indication of the extent to which a certain binary operation fails to be commutative.

Commutator and General linear group · Commutator and Orthogonal group · See more »

Commutator subgroup

In mathematics, more specifically in abstract algebra, the commutator subgroup or derived subgroup of a group is the subgroup generated by all the commutators of the group.

Commutator subgroup and General linear group · Commutator subgroup and Orthogonal group · See more »

Compact space

In mathematics, and more specifically in general topology, compactness is a property that generalizes the notion of a subset of Euclidean space being closed (that is, containing all its limit points) and bounded (that is, having all its points lie within some fixed distance of each other).

Compact space and General linear group · Compact space and Orthogonal group · See more »

Complex number

A complex number is a number that can be expressed in the form, where and are real numbers, and is a solution of the equation.

Complex number and General linear group · Complex number and Orthogonal group · See more »

Connected space

In topology and related branches of mathematics, a connected space is a topological space that cannot be represented as the union of two or more disjoint nonempty open subsets.

Connected space and General linear group · Connected space and Orthogonal group · See more »

Determinant

In linear algebra, the determinant is a value that can be computed from the elements of a square matrix.

Determinant and General linear group · Determinant and Orthogonal group · See more »

Dimension (vector space)

In mathematics, the dimension of a vector space V is the cardinality (i.e. the number of vectors) of a basis of V over its base field.

Dimension (vector space) and General linear group · Dimension (vector space) and Orthogonal group · See more »

Direct limit

In mathematics, a direct limit is a way to construct a (typically large) object from many (typically smaller) objects that are put together in a specific way.

Direct limit and General linear group · Direct limit and Orthogonal group · See more »

Field (mathematics)

In mathematics, a field is a set on which addition, subtraction, multiplication, and division are defined, and behave as when they are applied to rational and real numbers.

Field (mathematics) and General linear group · Field (mathematics) and Orthogonal group · See more »

Field with one element

In mathematics, the field with one element is a suggestive name for an object that should behave similarly to a finite field with a single element, if such a field could exist.

Field with one element and General linear group · Field with one element and Orthogonal group · See more »

Finite field

In mathematics, a finite field or Galois field (so-named in honor of Évariste Galois) is a field that contains a finite number of elements.

Finite field and General linear group · Finite field and Orthogonal group · See more »

Fundamental group

In the mathematical field of algebraic topology, the fundamental group is a mathematical group associated to any given pointed topological space that provides a way to determine when two paths, starting and ending at a fixed base point, can be continuously deformed into each other.

Fundamental group and General linear group · Fundamental group and Orthogonal group · See more »

Group (mathematics)

In mathematics, a group is an algebraic structure consisting of a set of elements equipped with an operation that combines any two elements to form a third element and that satisfies four conditions called the group axioms, namely closure, associativity, identity and invertibility.

General linear group and Group (mathematics) · Group (mathematics) and Orthogonal group · See more »

Group action

In mathematics, an action of a group is a formal way of interpreting the manner in which the elements of the group correspond to transformations of some space in a way that preserves the structure of that space.

General linear group and Group action · Group action and Orthogonal group · See more »

Identity component

In mathematics, the identity component of a topological group G is the connected component G0 of G that contains the identity element of the group.

General linear group and Identity component · Identity component and Orthogonal group · See more »

Identity matrix

In linear algebra, the identity matrix, or sometimes ambiguously called a unit matrix, of size n is the n × n square matrix with ones on the main diagonal and zeros elsewhere.

General linear group and Identity matrix · Identity matrix and Orthogonal group · See more »

Integer

An integer (from the Latin ''integer'' meaning "whole")Integer 's first literal meaning in Latin is "untouched", from in ("not") plus tangere ("to touch").

General linear group and Integer · Integer and Orthogonal group · See more »

Invertible matrix

In linear algebra, an n-by-n square matrix A is called invertible (also nonsingular or nondegenerate) if there exists an n-by-n square matrix B such that where In denotes the n-by-n identity matrix and the multiplication used is ordinary matrix multiplication.

General linear group and Invertible matrix · Invertible matrix and Orthogonal group · See more »

Lie algebra

In mathematics, a Lie algebra (pronounced "Lee") is a vector space \mathfrak g together with a non-associative, alternating bilinear map \mathfrak g \times \mathfrak g \rightarrow \mathfrak g; (x, y) \mapsto, called the Lie bracket, satisfying the Jacobi identity.

General linear group and Lie algebra · Lie algebra and Orthogonal group · See more »

Lie group

In mathematics, a Lie group (pronounced "Lee") is a group that is also a differentiable manifold, with the property that the group operations are compatible with the smooth structure.

General linear group and Lie group · Lie group and Orthogonal group · See more »

Linear map

In mathematics, a linear map (also called a linear mapping, linear transformation or, in some contexts, linear function) is a mapping between two modules (including vector spaces) that preserves (in the sense defined below) the operations of addition and scalar multiplication.

General linear group and Linear map · Linear map and Orthogonal group · See more »

List of finite simple groups

In mathematics, the classification of finite simple groups states that every finite simple group is cyclic, or alternating, or in one of 16 families of groups of Lie type, or one of 26 sporadic groups.

General linear group and List of finite simple groups · List of finite simple groups and Orthogonal group · See more »

Mathematics

Mathematics (from Greek μάθημα máthēma, "knowledge, study, learning") is the study of such topics as quantity, structure, space, and change.

General linear group and Mathematics · Mathematics and Orthogonal group · See more »

Matrix multiplication

In mathematics, matrix multiplication or matrix product is a binary operation that produces a matrix from two matrices with entries in a field, or, more generally, in a ring or even a semiring.

General linear group and Matrix multiplication · Matrix multiplication and Orthogonal group · See more »

Multiplicative group

In mathematics and group theory, the term multiplicative group refers to one of the following concepts.

General linear group and Multiplicative group · Multiplicative group and Orthogonal group · See more »

Normal subgroup

In abstract algebra, a normal subgroup is a subgroup which is invariant under conjugation by members of the group of which it is a part.

General linear group and Normal subgroup · Normal subgroup and Orthogonal group · See more »

Orientation (vector space)

In mathematics, orientation is a geometric notion that in two dimensions allows one to say when a cycle goes around clockwise or counterclockwise, and in three dimensions when a figure is left-handed or right-handed.

General linear group and Orientation (vector space) · Orientation (vector space) and Orthogonal group · See more »

Orthogonal group

In mathematics, the orthogonal group in dimension, denoted, is the group of distance-preserving transformations of a Euclidean space of dimension that preserve a fixed point, where the group operation is given by composing transformations.

General linear group and Orthogonal group · Orthogonal group and Orthogonal group · See more »

Quadratic form

In mathematics, a quadratic form is a homogeneous polynomial of degree two in a number of variables.

General linear group and Quadratic form · Orthogonal group and Quadratic form · See more »

Quotient group

A quotient group or factor group is a mathematical group obtained by aggregating similar elements of a larger group using an equivalence relation that preserves the group structure.

General linear group and Quotient group · Orthogonal group and Quotient group · See more »

Real number

In mathematics, a real number is a value of a continuous quantity that can represent a distance along a line.

General linear group and Real number · Orthogonal group and Real number · See more »

Semidirect product

In mathematics, specifically in group theory, the concept of a semidirect product is a generalization of a direct product.

General linear group and Semidirect product · Orthogonal group and Semidirect product · See more »

Simply connected space

In topology, a topological space is called simply connected (or 1-connected, or 1-simply connected) if it is path-connected and every path between two points can be continuously transformed (intuitively for embedded spaces, staying within the space) into any other such path while preserving the two endpoints in question.

General linear group and Simply connected space · Orthogonal group and Simply connected space · See more »

Subgroup

In group theory, a branch of mathematics, given a group G under a binary operation ∗, a subset H of G is called a subgroup of G if H also forms a group under the operation ∗.

General linear group and Subgroup · Orthogonal group and Subgroup · See more »

Symmetric group

In abstract algebra, the symmetric group defined over any set is the group whose elements are all the bijections from the set to itself, and whose group operation is the composition of functions.

General linear group and Symmetric group · Orthogonal group and Symmetric group · See more »

Symplectic group

In mathematics, the name symplectic group can refer to two different, but closely related, collections of mathematical groups, denoted and, the latter is called the compact symplectic group.

General linear group and Symplectic group · Orthogonal group and Symplectic group · See more »

Unitary group

In mathematics, the unitary group of degree n, denoted U(n), is the group of unitary matrices, with the group operation of matrix multiplication.

General linear group and Unitary group · Orthogonal group and Unitary group · See more »

Vector space

A vector space (also called a linear space) is a collection of objects called vectors, which may be added together and multiplied ("scaled") by numbers, called scalars.

General linear group and Vector space · Orthogonal group and Vector space · See more »

The list above answers the following questions

General linear group and Orthogonal group Comparison

General linear group has 120 relations, while Orthogonal group has 178. As they have in common 42, the Jaccard index is 14.09% = 42 / (120 + 178).

References

This article shows the relationship between General linear group and Orthogonal group. To access each article from which the information was extracted, please visit:

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