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From: Yang Yang on 12 May 2010 08:56
Hi, All

I have trouble to denote a vector that the index of its element is
defined as a element in a set.

For example, given a vector which index are in a set I={a,b,c}.

I want to define a vector that contains 3 elements V=[v_k | k \in
I]. Apparently, the order of element is not given.
So V=[v_a,v_b,v_c], So I can use normal operations like V_1+V_2=[v1_k
+v2_k | k\in I].


Do you know where I can find the conventional latex denotation for
this type of operation?


Best regards

Yang
From: Arturo Magidin on 12 May 2010 12:33
On May 12, 7:56 am, Yang Yang <comety...(a)gmail.com> wrote:
> Hi, All
>
> I have trouble to denote a vector that the index of its element is
> defined as a element in a set.
>
> For example, given a vector which index are in a set I={a,b,c}.
>
> I want to define a vector that contains 3 elements V=[v_k | k \in
> I].   Apparently, the order of element is not given.
> So V=[v_a,v_b,v_c], So I can use normal operations like V_1+V_2=[v1_k
> +v2_k | k\in I].
>
> Do you know where I can find the conventional latex denotation for
> this type of operation?

The "entries" of your V will be in some set S (probably the real
numbers or some field, since you are dealing with vectors). You
interpret the element [v_a,v_b,v_c] as a function from the index set I
to the set S; v_a is the image of a, v_b is the image of b, v_c is the
image of c. The addition you describe is then the usual "pointwise"
addition of functions: (v+w)(a) = v(a)+w(a), etc.

The set of all functions from I to S is denoted S^I; in LaTeX, this is
just $S^{I}$.

This agrees with the usual notion of tuples: R^n is the set of all
functions from n={0,1,2,3,...,n-1} to R, so it consists of functions
with "n" values (the n entries of the n-tuple).

--
Arturo Magidin

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