Some call them **currency exchange matrices**. From Boyd & Vandenberghe's [Introduction to Applied Linear Algebra][1]:

> **6.7** *Currency exchange matrix*. We consider a set of $n$ currencies, labeled $1,\dots,n$. (These might correspond to USD, RMB, EUR, and so on.) At a particular time the exchange or conversion rates among the $n$ currencies are given by an $n \times n$ (exchange rate) matrix $R$, where $R_{ij}$ is the amount of currency $i$ that you can buy for one unit of currency $j$. (All entries of $R$ are positive.) The exchange rates include commission charges, so we have $R_{ji} R_{ij} < 1$ for all $i \neq j$. You can assume that $R_{ii} = 1$. Suppose $y = Rx$, where $x$ is a vector (with nonnegative entries) that represents the amounts of the currencies that we hold. What is $y_i$? Your answer should be in English.

Note that you are considering currency exchange matrices where $R_{ij} R_{ji} = 1$, which one could call *perfect* currency exchange matrices. I would have written $R_{ij} R_{ji} \leq 1$ instead, in order to include the (reciprocal) perfect currency exchange matrices, too.

  [1]: https://web.stanford.edu/~boyd/vmls