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LieAlgebras[MatrixCentralizer] - find the matrix centralizer of a list of matrices

Calling Sequences

     MatrixCentralizer(M)

Parameters

     M   - a list of square matrices, each of the same dimension

 

Description

Examples

Description

• 

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(...).

Examples

withDifferentialGeometry:withLieAlgebras:

 

Example 1.

Find the Matrix centralizer of the set of matrices M1.

M1Matrix0,1,0,0

M10100

(2.1)

MatrixCentralizerM1

1001,0100

(2.2)

 

Example 2.

Find the Matrix centralizer of the set of matrices M2.

M2mapMatrix,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

M2001000000,001001000,110010000

(2.3)

MatrixCentralizerM2

100010001

(2.4)

See Also

DifferentialGeometry

LieAlgebras

Centralizer