# Is sub-vector an established mathematical entity?

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

• I haven't heard it before, but this 'sub-vector' seems appropriate term for that, I would accept and use it without hesitation.. – Berci Mar 12 '13 at 13:44
• You can call $\mathbf{X}$ a sequence, and then $\mathbf{Y}$ is a subsequence, which is standard. But when it can't cause any confusion, sub-vector sounds like a reasonable name too. – Alfonso Fernandez Mar 12 '13 at 13:52
• From the definition it doesn't seem that the order needs to be preserved, so sub-vector seems to be - indeed - more general than subsequence. I am not a mathematician, but has the prefix "sub" anything to do with a subspace that can be defined? Or is it free to use? – Anne van Rossum Mar 14 '13 at 9:22
• @AnnevanRossum 'sub-' is used in a lot of different ways (subgroup, subgraph, subword, subspace), it just generally means a 'smaller' version of an object that has the same kind of structure. – Jair Taylor Aug 2 '18 at 22:00

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 $v$.