Matrix with exactly one 1 in each row Is there a name associated to rectangular matrices $M \times N$ that have exactly one entry equal to $1$ in each row and $0$ everywhere else?
 A: Such a matrix is precisely a matrix representation of an arbitrary function from a set of size $M$ to a set of size $N$, in the sense that multiplication by a row vector is a linearized version of evaluating the function. 
A: For $M=N$, these are called permutation matrices. (striked according to Moron's comment) Yours are a (admittedly very restricted) special case of matrices with the consecutive ones property, but I'm not sure how much that helps you.
A: Wikipedia gives: "A right stochastic matrix is a square matrix each of whose rows consists of nonnegative real numbers, with each row summing to 1."
This definition restricts you to square matrices, but in Henryk Minc's book "Permanents" he explicitly considers non-square matrices and is always careful to say "$n$-square doubly stochastic" when he means this.
It fits in with Qiaochu Yuan's answer in that an arbitrary right stochastic matrix gives a 'function' where $M_{ij}$ is the probability that element $i$ in the domain is mapped to element $j$ in the co-domain.
