## Archive for October, 2012

### Better to have more input variables and less output variables

October 15, 2012

When trying to describe an invariant map $\phi : U \times V \to W$, where $U,V$ and $W$ are finite-dimensional spaces,  $\phi$ is “complicated” because its values are vector-valued. It is sometimes useful to look at $\phi^{\sharp} : U \times V \times W^{*} \to {\mathbb K}$, defined by $\phi^{\sharp}(u,v,w^*)=w^*(\phi(u,v))$. This map has more variables but takes scalar values.