basis matrix ourselves, then we can save the matrix that undoes the
process. And by undoing the process, we can get to a basis where
computations are fast again.
-
-Question: what's the best way to construct these algebras? We'll
-usually know,
-
- * the multiplication function
- * the inner-product function
- * a basis in either vector or matrix format
-
-and want:
-
- * an orthonormalized copy of the basis, in long-vector format
- * the reverse gram-schmidt matrix that deorthonormalizes that
- long-vector basis
- * a multiplication matrix (for speed) w.r.t. the orthonormal basis
- * an inner-product matrix (for speed) w.r.t. the orthonormal basis
- * a way to turn those two matrices into multiplication and inner-
- product matrices for the deorthonormalized basis.