8

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

Anne van Rossum
  • 791
  • 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 09:22
  • @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 02 '18 at 22:00

1 Answers1

4

"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.

NoName
  • 2,975