TITLE: Is sub-vector an established mathematical entity?
QUESTION [6 upvotes]: Reading the following paragraph I was wondering how this entity that the authors [1] call a sub-vector should be named. In Matlab a sub-vector has to be contiguous. 

Let $\mathbf{X}=(X_1,\ldots,X_n)$ be a vector of random variables and $\mathbf{x}=(x_1,\ldots,x_n)$ a possible value setting (configuration) for these variables. $x_i$ denotes a possible value of $X_i$, the $i$th component of $\mathbf{X}$, and $\mathbf{y}$ denotes a possible value setting for the sub-vector $\mathbf{Y}=(X_{J_1},\ldots,X_{J_k})$, $J=\{J_1,\ldots,J_k\}\subseteq\{1,\ldots,n\}$.

Is sub-vector indeed the proper mathematical term for this entity?
[1] A review of probabilistic graphical models in evolutionary computation [Larrañaga et al.], 2012

REPLY [3 votes]: "Subvector" doesn't seem to have a standard definition. As you've noted, it's different in Matlab.
According to some authors (eg. Dominic Welsh in his book Matroid Theory), a subvector is a vector that's in the same general direction as another vector, but shorter. To be more precise, let $u = (u_1, u_2, \dots, u_n)$ and let $v = (v_1, v_2, \ldots, v_n)$. If each $v_i - u_i$ is nonnegative, then $u$ is a subvector of $v$.
The conclusion is that if you're going to use the term "subvector", it's best to define it first.