  In this paper, we study the Poisson equation and heat equation in a model
matrix geometry $M_n$. Our main results are about the Poisson equation and
global behavior of the heat equation on $M_n$. We can show that if $c_0$ is the
initial positive definite matrix in $M_n$, then $c(t)$ exists for all time and
is positive definite too. We can also show the entropy stability of the
solutions to the heat equation.
