LieAlgebras[MatrixNormalizer] - find the matrix normalizer of a list of matrices
Calling Sequences
MatrixNormalizer(M, A)
Parameterss
M - a list of square matrices, each of the same dimension
A - (optional) a list of square matrices, each of the same dimension, containing the matrices M, and forming a Lie algebra
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Description
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A list of vectors defining a basis for the normalizer of is returned.
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The command MatrixNormalizer is part of the DifferentialGeometry:-LieAlgebras package. It can be used in the form MatrixNormalizer(...) only after executing the commands with(DifferentialGeometry) and with(LieAlgebras), but can always be used by executing DifferentialGeometry:-LieAlgebras:-MatrixNormalizer(...).
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Examples
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Example 1.
Find the normalizer of the set of matrices M1.
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| (2.1) |
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| (2.2) |
Example 2.
Find the normalizer of the set of matrices M2 within the Lie algebra A.
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| (2.3) |
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| (2.4) |
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| (2.5) |
We use the LieAlgebraData command to calculate the commutation relations for the Lie algebra of matrices
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| (2.6) |
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