Example 1.
We check if each matrix in a list of matrices belongs to
With the keyword argument output = 'integer' , 0 is returned if all the matrices belong to the specified matrix algebra, otherwise the position of the first matrix which does not belong to the specified matrix algebra is returned.
Example 2.
We check if each matrix in list of matrices belong to . This is the Lie algebra of 4×4 matrices which are skew-symmetric with respect to a quadratic form of signature [2,2]. The default choice for the quadratic form is . With the keyword argument version = 2, the quadratic form is used. With the keyword argument quadraticform = , the quadratic form (a 4×4 symmetric matrix with signature [2, 2]) is used.
1. Default option.
2. with version = 2.
3. with quadraticform = M
Example 3.
We check if the members of a list of matrices belong to This is the real Lie algebra of matrices which are skew-symmetric with respect to a skew-symmetric matrix . The default choice is . Other forms for can be specified with the keyword argument skewform =
Here is the standard form of the matrices for .
Define a skew-symmetric matrix .
Here is the form of the matrices for with respect to
Example 4.
Check that a list of matrices consists of upper triangular matrices.
Example 5.
Check that a list of matrices consists of nilpotent matrices.
Example 6.
Check that the following matrices define a Lie algebra and that this representation is unitary.
