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$$f(x) = cos(x)$$

I'd like to write something like:

$$f(\vec{x}) = \begin{pmatrix}

f_1(x_1) \\

f_2(x_2) \\

... \\

f_n(x_n)

\end{pmatrix} $$

where ##f_i## is some nonlinear function on ##x_i## like ##cos(x_i)##.

Or, if you will...

$$f(\vec{x}) = f_1(x_1) + f_2(x_2) + ... + f_n(x_n)$$

or even more wild linear and non-linear manipulations of ##x_i##.

Would appreciate any help in finding resources on this topic. I don't even know what the name of this particular area of interest is, assuming it has one.