Symmetrizing, alternating, wedging

A square matrix decomposes into symmetric and skew-symmetric part. ΤS and ΤA perform these linear projections.

symmetric | skew symmetric | original |

The functions ΤS and ΤA that symmetrize and alternate work for tensors of arbitrary rank but with fixed dimension. For instance, consider the (0,4)-tensor X below. Due to its length, we do not show X, but we indicate that S(A(X))=A(S(X))=0.

DGkernel encodes wedging of two tensors as

When wedging multiple tensors, use brackets. Have a look at the following simple example.

The following line of code sets up the tri/multi-linear-form that represents the determinant of 3×3 matrices.

Lets go two ways to obtain the determinant of the matrix X below.

Created by Mathematica (September 30, 2006) |