Hi David, On Jul 6, 2004, at 10:24 AM, David B. Held wrote:
Actually, taking a look at mathworld.wolfram.com and a few other sites, I have reached the tentative conclusion that outer products can only be formed over vectors, not matrices. Matrix multiplication is well-defined and unambiguous, whereas vector multiplication comes in at least four varieties: dot product, cross product (also called the "outer product"), perpendicular dot product, and vector direct product.
Thanks for the concise summary!
Hence, it would make sense that operator*(matrix, matrix) would mean "matrix multiplication".
yes.
However, operator*(vector, vector) is the problem child.
Yes, there is no obvious "right choice" for vectors. There are basically two options, both of which are fine by me. 1. Use names such as inner_product (or dot_product), outer_product, etc. This approach is "true" to the mathematics and completely unambiguous. 2. Take the Matlab approach (which also appears in many textbooks), and treat vectors as degenerate matrices: as either row or column vectors. In this case, operator* on these vectors just has the usual meaning it does for matrices. Depending on whether the vectors are row or column vectors determines whether operator* is equivalent to inner or outer product. This approach is more concise and fits with existing practice. Cheers, Jeremy _______________________________________________ Jeremy Siek <jsiek@osl.iu.edu> http://www.osl.iu.edu/~jsiek Ph.D. Student, Indiana University Bloomington C++ Booster (http://www.boost.org) _______________________________________________