A right stochastic matrix $A$ is a square matrix with entries from the unit interval, and whose rows add to $1$. They are used in Markov Chain problems, of course.
Is there a name for matrices of the form $B = I-A$ (where $I$ is the identity matrix of appropriate size)? Such a matrix might arise when calculating the expected number of transitions to reach a certain state. You might have a system of equations of the form
$E_a = 1 + \frac{1}{2}E_b + \frac{1}{4}E_c + \frac{1}{4}E_d$.
Here $a$ is a particular state, $E_a$ is the expected number of turns to reach some particular "terminal" state when currently at state $a$, and the probability of transitioning from $a$ to $b$ is $\frac{1}{2}$, from $a$ to $c$ is $\frac{1}{4}$, and so on. It is not hard to see that the resulting linear system has a matrix representation of the form $I-A$.
This seems like a natural idea but I haven't been able to find references or appropriate terminology, if it exists.