Hi, I have a rather trivial question but google did not really help me. So far I was always familiar with the fact that the determinant of a square matrix is positive. But it is not. When I randomly execute det(randn(12)) in MATLAB I get a negative determinant every couple of trials. What is the meaning of a negative determinate? And is it allowed to take the absolute value in this case? For example, in a convex optimization problem, you often maximize the log-determinant of a matrix. But in order for this to be defined, the determinant should be positive. Even worse, if I have a complex matrix, the determinant is generally complex too. For example, executing "det(randn(12)+i*randn(12))" in MATLAB always gives a complex determinant. Similarly to above: How to interpret a complex determinant, what does it tell me? And if my matrix in such a convex optimization problem is complex, log(det(A)) will also be complex. Since ">" for complex numbers is defined as the absolute value anyway, am I allowed to take the absolute value of the determinant, i.e., "log(abs(det(A)))" ?