# The relation between trace and determinant of a matrix

Let $M$ be a symmetric $n \times n$ matrix.

Is there any equality or inequality that relates the trace and determinant of $M$?

Not exactly what you’re looking for but I would be remiss not to mention that for any complex square matrix $A$ the following identity holds:
$$\det(e^A)=e^{\mbox{tr}(A)}$$