  To better understand the algebra $\mathcal{M}_n$ of all $n\times n$ complex
matrices, we explore the class of accretive matrices. This class has received
renowned attention in recent years due to its role in complementing those
results known for positive definite matrices. More precisely, we have several
results that allow a better understanding of accretive matrices. Among many
results, we present order-preserving results, Choi-Davis-type inequalities,
mean-convex inequalities, sub-multiplicative results for the real part, and new
bounds of the absolute value of accretive matrices. These results will be
compared with the existing literature. In the end, we quickly pass through
related entropy results for accretive matrices.
