Initialize a 4-dimensional manifold M with coordinates [x, y, z, w].
Example 1.
Find a basis B1 for the span of the vectors in S1.
Use the GetComponents command to check that each vector in S is a unique linear combination of the vectors in B. (GetComponents returns the coefficients of the vectors in S as linear combination of the vectors in B. If one of the vectors in S is not a linear combination of the vectors in B, an empty list [] is returned).
The basis B1 is not the simplest basis for S1. Another choice of basis for S1 can be found using the command CanonicalBasis.
Example 2.
Find a basis for the span of the tensors in S2.
Example 3.
DGbasis also accepts a list of Matrices or Vectors.
Example 4.
Here is the basis for S4 using function coefficients.
Here is the basis for S4 using real number coefficients.