# Confusion in Notation for Array and Dimension

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 "$$\hat{x}$$"?

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.
• 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 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
• @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