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I have a vector $\mathbf{x} = (x_1,x_2)$, how do I represent the array of such vector?

Is it $\mathbf{x} \in \mathbf{X}$ where $\mathbf{X}$ = $\bigcup _{{1}}^{k}\mathbf{x}^s$ for $s \in (1,..k)$ length of $k$ vectors? Something seems off here!

Also I want to index a vector in array then is this correct way to represent the index ${\mathbf{x}^1}$? and the corresponding dimensional representation of this index shall be $(x_1^1,x_2^1)$?

Is the usage of "hat" appropriate here ? such as "$\hat{x}$"?

user0193
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1 Answers1

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I'm not sure if by "array of vectors" you intend a single row with the vectors listed, or if you mean a rectangular array with the components as entries or what. But I think the most common thing one would do in a situation like this is to put them in a rectangular matrix and use double indices.

That is, you would have $m$ vectors with $n$ components that look like $(x_{i,1}, \ldots, x_{i, n})$ for $i\in \{1\ldots m\}$, so that the rows of your matrix are the original $n$-tuples.

I have no idea why one would use a hat decorator in this case.

rschwieb
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  • By array of vectors I mean $[\mathbf{x_i}]$ for $i \in {1,..,m}$ so its not rectangular matrix, just vector listed. So will the expanded form be $[(x_{1,i},x_{2,i})]$ $i \in {1,..,m}$ ? – user0193 Sep 30 '20 at 19:04
  • I can think of no better way to write the concatenation as $(x_{1,1},\ldots, x_{1, n},x_{2,1},\ldots x_{2, n},\ldots,x_{m, 1},\ldots x_{m, n})$, or maybe just as $(\mathbf{x_1},\dots,\mathbf{x_m})$ where $\mathbf {x_i}=(x_{i,1},\ldots,x_{i,n})$ – rschwieb Sep 30 '20 at 19:25
  • noted. Thanks and also does this makes sense $\mathbf{x} \in \mathbf{X}$ where $\bigcup _{{1}}^{k}\mathbf{x}^s$ for $s i\in {1\ldots k}$? – user0193 Sep 30 '20 at 19:39
  • @JhonnyS No, it doesn't. – rschwieb Sep 30 '20 at 20:07
  • sorry, i mean $\mathbf{x}^s \in \mathbf{X}$ where $ \mathbf{X}=\bigcup _{{1}}^{k}\mathbf{x}^s$ for $s \in {1\ldots k}$ – user0193 Sep 30 '20 at 20:25
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    @JhonnyS I think using $\bigcup$ is wildly confusing and not helpful. I'm not sure what's out there in terms of a symbol for a concatenation operation, but almost anything is better than $\bigcup$. Even something like $\boxplus$. At any rate you would have to explain that's what you meant, since the notation might not be common. – rschwieb Sep 30 '20 at 20:27
  • noted. I was just implying that $\mathbf{X}$ is a set formed by concatenating all the $\mathbf{x}$'es so say we have the length for the set 5 i.e. $\mathbf{x^1}..\mathbf{x^5}$ the union of all of them forms $\mathbf{X}$ where $\mathbf{X}=\bigcup _{{s=1}}^{s=5}\mathbf{x}^s$ – user0193 Sep 30 '20 at 20:30
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    @JhonnyS I can see where you're coming from, but for the sanity of the people listening to you, don't call $X$ a set and don't use $\bigcup$. Use something that suggests appending more, like $\oplus$ or $\boxplus$. – rschwieb Sep 30 '20 at 20:36