LieAlgebras[MatrixCentralizer] - find the matrix centralizer of a list of matrices
M - a list of square matrices, each of the same dimension
The centralizer of a set of matrices M is the Lie algebra of matrices which commute with all the matrices in M.
A list of matrices defining a basis for the centralizer of M is returned.
The command MatrixCentralizer is part of the DifferentialGeometry:-LieAlgebras package. It can be used in the form MatrixCentralizer(...) only after executing the commands with(DifferentialGeometry) and with(LieAlgebras), but can always be used by executing DifferentialGeometry:-LieAlgebras:-MatrixCentralizer(...).
Find the Matrix centralizer of the set of matrices M1.
M1 ≔ Matrix⁡0,1,0,0
Find the Matrix centralizer of the set of matrices M2.
M2 ≔ map⁡Matrix,0,0,1,0,0,0,0,0,0,0,0,1,0,0,1,0,0,0,−1,−1,0,0,−1,0,0,0,0
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