In linear agebra, is there a special name to matrices $M$ of the form
$$M = \begin{pmatrix} a_{11} & 0 & \cdots & 0 \\ 0 & a_{22} & \cdots & 0 \\ \vdots & \vdots & \ddots & \vdots \\ 0 & 0 & \cdots & a_{nn} \end{pmatrix}$$
with $\text{Trace}(M) = a_{11}+a_{22}+\ldots+a_{nn} =1$ and $M$ is a diagonal square matrix with entries $0 \leq a\leq 1 \in \mathbb{R}$?
Moreover what are some basic or interesting properties that these matrices exhibit? I'm looking for any general interesting known things like properties of its characteristic polynomial, minimal polynomial,... Any insights or interesting remarks are appreciated!