Mathematical equivalent of Matlab special case element-wise multiplication similar to Schur-product

Question

I'm searching for the mathematical name and notation of a special case of the element-wise multiplication .* in Matlab shown in the following picture:

Desired Operation

I'm aware that this would be called Hadamard- or Schur-product for the case of equal dimensions but how can this operation be denoted for cases like the given one?

Thanks.

Answer 1

I've never seen a standard notation for this, but you could easily define one. Let $f: \mathbb{R}^2 \to M_{2\times 2}$ send $(\alpha, \beta)$ to the diagonal matrix with those entries. Then your operation is $$A \,.^*\, v = f(v)A.$$