representation theory
Sign in to savebranch of mathematics that studies representations of abstract algebraic structures as linear transformations on vector spaces
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Vinony's link graph records 764 inbound references to representation theory, and connects out to linear map, Lie algebra and vector space.
Vinony files it under Algebraic structures and Representation theory.
Vinony links it to 29 Wikipedia language editions.
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- Category:Representation theory
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Encyclopedic overview
Representation theory studies how algebraic structures "act" on objects. A simple example is the way a polygon is transformed by its symmetries under reflections and rotations, which are all linear transformations about the center of the polygon.
Representation theory is a branch of mathematics that studies abstract algebraic structures by representing their elements as linear transformations of vector spaces, and studies modules over these abstract algebraic structures. In essence, a representation makes an abstract algebraic object more concrete by describing its elements by matrices and their algebraic operations (for example, matrix addition, matrix multiplication).
Excerpted from Wikipedia’s “representation theory” article, available under the CC BY-SA 4.0 licence.