Notation for the all-ones vector - MathOverflow most recent 30 from http://mathoverflow.net 2013-06-20T02:40:46Z http://mathoverflow.net/feeds/question/9898 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/9898/notation-for-the-all-ones-vector Notation for the all-ones vector Bkkbrad 2009-12-27T21:14:53Z 2009-12-28T16:33:56Z <p>What's the most common way of writing the all-ones vector, that is, the vector, when projected onto each standard basis vector of a given vector space, having length one? The zero vector is frequently written $\vec{0}$, so I'm partial to writing the all-ones vector as $\vec{1}$, but I don't know how popular this is, and I don't know if a reader might confuse it with the identity matrix.</p> <p>I'm writing for a graph theory audience, if that helps pick a notation.</p> http://mathoverflow.net/questions/9898/notation-for-the-all-ones-vector/9900#9900 Answer by Anton Petrunin for Notation for the all-ones vector Anton Petrunin 2009-12-27T21:31:09Z 2009-12-27T21:31:09Z <p>Once I had the same problem, I used notation similar to yours: $\mathbf{0}$ for zero-vector and $\mathbf{1}$ for "all-ones vector".</p> <ul> <li><p>It is NOT common, so you have to define it</p></li> <li><p>I would not do it unless you have many formulas with it --- if you use it just few times denote it by some letter...</p></li> </ul> http://mathoverflow.net/questions/9898/notation-for-the-all-ones-vector/9902#9902 Answer by Greg Kuperberg for Notation for the all-ones vector Greg Kuperberg 2009-12-27T21:34:06Z 2009-12-27T21:49:50Z <p>I have used the notation $\vec{1}$ in a paper. I think that it's a good choice if you help the reader by defining it. I did a Google Scholar such of "vector of all ones", and I found a lot of so-so notation such as $e$, $u$, $\mathbf{e}$, $\mathbf{1}$, and even just plain $1$. I don't think that the literature is loyal to any particular choice. Confusing $\vec{1}$ with a matrix would be a little strange, because a matrix is suggested by a two-headed arrow, or $\stackrel{\leftrightarrow}{1}$.</p> http://mathoverflow.net/questions/9898/notation-for-the-all-ones-vector/9904#9904 Answer by Chris Godsil for Notation for the all-ones vector Chris Godsil 2009-12-27T21:38:56Z 2009-12-27T21:38:56Z <p>I use \mathbf{1} in papers (and in books) In combinatorics it is also common to use $j$, and to use $J$ for the all-ones matrix. Using $j$ for the all-ones vector has obvious problems since it occurs so often as an index. No solution is perfect, but I find I have fewer problems with \mathbf{1}. </p> <p>I agree you should define it.</p> <p>Generally I avoid using decorations (tildes, arrows,...) to represent vectors - they look really ugly on the page.</p> http://mathoverflow.net/questions/9898/notation-for-the-all-ones-vector/9908#9908 Answer by Mariano Suárez-Alvarez for Notation for the all-ones vector Mariano Suárez-Alvarez 2009-12-27T22:42:00Z 2009-12-27T22:42:00Z <p>I like \mathbb'ed ones for this. You can use the <a href="http://www.ctan.org/tex-archive/help/Catalogue/entries/mathbbol.html" rel="nofollow">mathbbol package</a> by simply saying \mathbb{1}.</p> http://mathoverflow.net/questions/9898/notation-for-the-all-ones-vector/9919#9919 Answer by Douglas S. Stones for Notation for the all-ones vector Douglas S. Stones 2009-12-28T00:00:43Z 2009-12-28T00:00:43Z <p>Clearly there's no consensus on this issue. Personally, I dislike bold-face anything in papers as it's often hard for the reader to tell whether it's bold-face or not (not everyone has a decent printer + good eyesight). I would use $\vec{1}$ myself, but it doesn't matter so much, as long as its defined appropriately.</p> http://mathoverflow.net/questions/9898/notation-for-the-all-ones-vector/9925#9925 Answer by Ilya Nikokoshev for Notation for the all-ones vector Ilya Nikokoshev 2009-12-28T00:55:01Z 2009-12-28T00:55:01Z <p>I'd say, denote it any way, but please make clear in the introduction that it depends on the basis!</p> http://mathoverflow.net/questions/9898/notation-for-the-all-ones-vector/9963#9963 Answer by Scott Carter for Notation for the all-ones vector Scott Carter 2009-12-28T16:33:56Z 2009-12-28T16:33:56Z <p>Let $I \subset \{ 1,2,3,\ldots, n \}$. Let $e_I = \sum_{i\in I} e_i.$ Let $[n]=\{ 1,2,3, \ldots, n \}$. Then $\vec{1}=e_{[n]}$. Also $e_{\{i\}} = e_i$. This is not satisfactory to your context, but may have the advantage of alternative usages in subsequent contexts. </p>