Better to have more input variables and less output variables

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.

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Ewan Delanoy's mathematical blog