Figure 1
The logic of determining MS6. (a) E3toS6 is an operator that will generate a vector s in S6 from a vector e in E3×3. (b) E is a matrix operating on E3×3 and S is a matrix operating on S6. Correspondingly, we can rewrite (a) in this more general form. (c) Choosing as an example the first basis vector ([1, 0, 0, 0, 0, 0]) in the list of basis vectors, we can then multiply by S. The first column of elements of S can then be placed into the matrix as indicated. (d) In like manner, we can multiply the first basis vector expressed in E3×3 by the matrix E in E3 that corresponds to the matrix S. However, in this case, the elements of MS6 can be computed from the list of calculations above for the first basis vector and the values of matrix E. Repeating this process for each of the six basis vectors completes S. |