# Why is the matrix of all 1's called “J”? [closed]

I've seen J referenced recently in some discussion about algebraic combinatorics, and it took me a while to figure out it was the matrix of all ones. It came up without definition, and I spent too long trying to google "what is a J matrix".

I found this, but I can find no reference to the convention of using J to represent the matrix. Maybe it's arbitrary?

https://en.wikipedia.org/wiki/Matrix_of_ones

## closed as off-topic by YCor, Steven Landsburg, Dima Pasechnik, Pace Nielsen, Jan-Christoph Schlage-PuchtaJan 24 at 19:58

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• One guess is that the identity matrix already has a well-established claim on the more natural-seeming "I", so "J" is the next alternative. – Noam D. Elkies Jan 24 at 3:11
• Probably something to do with choices made by people creating computer algebra systems? – David Roberts Jan 24 at 5:55
• At least it is not an 'O' for "all Ones". – Per Alexandersson Jan 24 at 11:03
• Perhaps it's from Jednostka, the Polish word for unit. – Gerry Myerson Jan 24 at 11:38
• See the related question (which has a bunch of answers, then ended up being closed) mathoverflow.net/questions/9898/… – Joe Silverman Jan 24 at 12:48

• $$1$$, $$\mathbf 1$$ or $$\mathbb 1$$ but these are usually a danger for confusion with the scalar and the latter one is often used to represent the all-1s-vector already.
• a letter similar to 1, e.g. $$I$$, $$\mathbf I$$ or $$\mathbb I$$, but these are usually used for the identity matrix already.
So you go with the next best letter that resembles a "1" $$-$$ namely $$J$$. However, I also have seen $$E$$. I would say that if you have some experience in the topic, you can spot this from the context. But a well-written text would introduce this notation nevertheless.
• Unfortunately $E$ is also commonly used for a matrix with only one non-zero entry (often subscripted, like $E_{i j}$). – LSpice Jan 24 at 14:57