On Mon, Jun 19, 2006 at 08:30:00PM -0700, Frederick Akalin wrote:

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Having rank also solves the following problem I was wondering about: how do you define vector scalar multiplication in a sufficiently restrictive way. Without a notion of rank, matrix * vector could be ambiguous with scalar * vector since (matrix * x, matrix * y, matrix * z) would be a valid vector<matrix<T> >.

Perhaps I'm horribly misunderstanding something, but wouldn't the fact that "matrix<T> * vector<T>" has to return "vector<T>" be enough to disambiguate it? Your example is implying that matrix<T> * vector<T> can somehow return vector<matrix<T> >.

Oops, left out the context. If you want general support for units, but also want the vector classes completely decoupled from units, you'll need to be able to multiply things like matrix<float> * vector<length> or matrix<stress / area> * vector<area>. You also want to be able to multiple a scalar with arbitrary units times a vector to get another scalar. The scalar multiplication function will look something like template<class S,class T> vector<typeof(S*T>)> operator*(const S& s,const vector<T>& v) { return vector<typeof(S*T)>(s*v.x,s*v.y,s*v.z); } but this function works perfectly well if you plug in S = matrix, so it has to be restricted in some way. Geoffrey