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Additional
Group representations
English Wikipedia - The Free Encyclopedia
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Group representation
In the
mathematical
field of
representation theory
,
group representations
describe abstract
groups
in terms of
linear transformations
of
vector spaces
; in particular, they can be used to represent group elements as
matrices
so that the group operation can be represented by
matrix multiplication
. Representations of groups are important because they allow many
group-theoretic
problems to be
reduced
to problems in
linear algebra
, which is well understood. They are also important in
physics
because, for example, they describe how the
symmetry group
of a physical system affects the solutions of equations describing that system.
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