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Given a function $f(x)=y$ is correct to say that $f\left(\left[\begin{array}{c} x_1 \\ x_2 \\ x_3 \end{array}\right]\right)=\left[\begin{array}{c} y_1 \\ y_2 \\ y_3 \end{array}\right]$?

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Also, it is often more convenient to write $f([x_1,x_2,x_3]^T) = [y_1,y_2,y_3]^T$ in case of long vertical vectors. –  dtldarek Jun 23 '12 at 11:21
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up vote 3 down vote accepted

Yes, assuming that $x \in A^3$ and $y \in B^3$ for some suitable spaces $A,B$ you just give the explicit representation of those elements which is equivalent to actually writing $x$ or $y$.

If you want to make it even more formal you can say for example that the $x_i$ represent the coordinate entries of $x$, but that is common notation anyways and most people will understand it.

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Unfortunately $x\in R$ and $y\in R$. Sorry, I wasn't clear in my question. –  Paulo Fracasso Jun 22 '12 at 14:39
    
Do you mean $x,y \in \mathbb{R}^3$? Then the answer remains the same. Otherwise you have to explain how you define $[x_1,x_2,x_3] \in R$ –  Listing Jun 22 '12 at 14:58
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