I was working on a statistical subject and we consider a vector $z\in\mathbb{R}^d$, at some point we want to distinguish the k first elements of this vector, thus the author wrote $z$ as $z'=[z_{1}^{'} z_{2}^{'}]$ where $z_{1}^{'}$ represents the k first elements of interest. However I don't know what is the nature of $z'$, is this a "matrix notation" in order to cut a vector in two "subset" ?
Thank you a lot
A formal answer is as follows: the vector spaces $\mathbb{R}^d$ and $\mathbb{R}^{k}\times \mathbb{R}^{d-k}$ are canonically isomorphic (as vector spaces). This means that both vector spaces represent essentially the same vector space, so the elements of $\mathbb{R}^d$ can be identified uniquely with elements of $\mathbb{R}^{k}\times \mathbb{R}^{d-k}$ and viceversa. This mean that for every $v\in \mathbb{R}^d$ there is a unique $v'\in \mathbb{R}^k \times \mathbb{R}^{d-k}$ that represents canonically $v$, where $v'=(v_1,v_2)$ for some $v_1\in \mathbb{R}^k$ and $v_2\in \mathbb{R}^{d-k}$.