Matrix and symmetry groups
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Some special matrix groups
Equations are omitted for technical reasons - download the original pdf
The general orthogonal group The general orthogonal group is the name given to the group of matrices that satisfiy the property [Equation goes here - download the original to see it.] If it can be shown that the general orthogonal group comprises all rotation and reflection matrices. That is, all matrices of the for [Equation goes here - download the original to see it.] and all matrices of the form [Equation goes here - download the original to see it.] The general rotation group The general rotation group is a subset of the general orthogonal group and is the group comprising all rotation matrices [Equation goes here - download the original to see it.] Symmetry groups To each symmetry group of a plane figure there corresponds a matrix group. For example, the symmetry group of an equilateral triangle defines a matrix group [Diagram goes here - download the original to see it.] [Diagram goes here - download the original to see it.] Thus S3 is the matrix group [Equation goes here - download the original to see it.] under matrix multiplication
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Contents of
Matrix and symmetry groups
1 The idea of a matrix group
2 Some special matrix groups
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