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General linear group and Manifold

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

Difference between General linear group and Manifold

General linear group vs. Manifold

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, a manifold is a topological space that locally resembles Euclidean space near each point.

Similarities between General linear group and Manifold

General linear group and Manifold have 17 things in common (in Unionpedia): Algebraic variety, Betti number, Bijection, Compact space, Complex number, Connected space, Continuous function, Differentiable manifold, Group (mathematics), Group action, Hilbert space, Lie group, Mathematics, Orthogonal group, Real number, Simply connected space, Volume.

Algebraic variety

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

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

Betti number

In algebraic topology, the Betti numbers are used to distinguish topological spaces based on the connectivity of n-dimensional simplicial complexes.

Betti number and General linear group · Betti number and Manifold · See more »

Bijection

In mathematics, a bijection, bijective function, or one-to-one correspondence is a function between the elements of two sets, where each element of one set is paired with exactly one element of the other set, and each element of the other set is paired with exactly one element of the first set.

Bijection and General linear group · Bijection and Manifold · 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 Manifold · 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.

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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 Manifold · See more »

Continuous function

In mathematics, a continuous function is a function for which sufficiently small changes in the input result in arbitrarily small changes in the output.

Continuous function and General linear group · Continuous function and Manifold · See more »

Differentiable manifold

In mathematics, a differentiable manifold (also differential manifold) is a type of manifold that is locally similar enough to a linear space to allow one to do calculus.

Differentiable manifold and General linear group · Differentiable manifold and Manifold · 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 Manifold · 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 Manifold · See more »

Hilbert space

The mathematical concept of a Hilbert space, named after David Hilbert, generalizes the notion of Euclidean space.

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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 Manifold · See more »

Mathematics

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

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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 · Manifold and Orthogonal 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.

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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 · Manifold and Simply connected space · See more »

Volume

Volume is the quantity of three-dimensional space enclosed by a closed surface, for example, the space that a substance (solid, liquid, gas, or plasma) or shape occupies or contains.

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The list above answers the following questions

General linear group and Manifold Comparison

General linear group has 120 relations, while Manifold has 286. As they have in common 17, the Jaccard index is 4.19% = 17 / (120 + 286).

References

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