# Functions applied from the right

In some of the older books by Nathan Jacobson (like Lie Algebras and Lectures in Abstract Algebra), a convention is used that is quite uncommon at least today: Functions are applied from the right. For instance, a map $\theta$ applied to an object $x$ is written $x\theta$, sometimes even $x^\theta$. I do indeed see the benefits of this notation: Functions are applied from left to right, which is a nice analogue to the notation $$\theta\gamma\colon x\stackrel\theta\longmapsto x\theta\stackrel\gamma\longmapsto x\theta\gamma.$$ However, it does not make the notation any less difficult to get used to. I was wondering if this notation was ever very common, or if it is just some Jacobson thing? Has anyone seen it elsewhere, and do you know its origin (if it has one)?

• As a side note, Jacobson appears to have abandoned the convention in his later works. In Finite-Dimensional Division Algebras over Fields, functions are applied from the left. – Gaussler Mar 12 '15 at 18:57
• I would say it was more common in the 1960s and early 1970s. I have not seen it in any recent works. – Zhen Lin Mar 12 '15 at 20:13

In coding theory, codewords are often expressed as row vectors. Mappings are sometimes done by matrices. So the input (row vector) is on the left and the function (matrix) is on the right. $\vec{v}M$.