I know this is loose and generic, but I just need to check my logic and if there is any reference or method ye may refer to, will be very much appreciated.
I have a function $f(\vec{v})$ which only works for $\vec{v} \in {\rm I\!R}^3$.
The problem is that I have another vector $\vec{u} = \{a_1, a_2, a_3, a_4, a_5, a_6\}\in {\rm I\!R}^6$ which I need to process by that function.
My question:
Does it make sense mathematically to perspective project the first three dimensions and get $\vec{u^\prime} = \{a_1^\prime, a_2^\prime , a_3^\prime\} \in {\rm I\!R}^3$ , and to project the second three dimensions and get $\vec{u^{\prime\prime}} = \{a_4^{\prime\prime}, a_5^{\prime\prime} , a_6^{\prime\prime}\} \in {\rm I\!R}^3$. Then apply $f(\vec{u^\prime})$ and $f(\vec{u^{\prime\prime}})$. And finally define a function $g(f(\vec{u^\prime}), f(\vec{u^{\prime\prime}}))$ to process the results (e.g. sum, mean or variance..etc)?
Or if there is any other approach, hints or suggestions?
Many Thanks.
The process you describe is perfectly valid from a purely formal point of view. However, to decide whether it makes sense we need more context. What are you trying to do? What do those vectors represent? What do you hope to accomplish?