DGbasis(S, option)

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.

DifferentialGeometry, CanonicalBasis, GetComponents