I would like to formulate the following in proper math notation, but I am not sure how to do so. Maybe you can help me with this.
I have a set of data D and some additional arguments r_i and a function f, that calculates 2 values a and b from this data. Basically I have a, b = f(r_1, r_2, D).
How would you format this in proper math notation?
You have a set $\Omega$ of data points $\omega$ and the parameter points $r=(r_1,r_2)\in{\mathbb R}^2$. You then are given two functions $$f:\quad{\mathbb R}^2\times\Omega\to {\mathbb R}^n, \qquad(r,\omega)\to a(r,\omega)=\bigl(a_1(r,\omega),\ldots, a_n(r,\omega)\bigr)$$ and $$g:\quad{\mathbb R}^2\times\Omega\to M_{m\times n}, \qquad(r,\omega)\to B(r,\omega)=\bigl[b_{ik}(r,\omega)\bigr]_{i\in[m],\> k\in[n]}\ .$$