# What does Determinant of Covariance Matrix give?

I am representing my 3d data in covariance matrix. I just want to know what the determinant of a covariance matrix gives. If the determinant is positive, zero, negative, high positive, high negative, what does it mean or represent?

Thanks

EDIT:

Covariance is being used to represent variance for 3d coordiantes that I have. For example, covariance matrix A determinant is +100, and covariance matrix B determinant is +5. Which of these values show if the variance is more? Which value tells that datapoints are more dispersed? Which value shows that readings are further away from mean?

• See this answer for a comparison of the trace and determinant of the covariance matrix as two measures for total variance. – caracal Aug 7 '14 at 7:02

The determinant of the covariance matrix is the generalized variance. This means it is like a scalar variance when the dimension is 1. Thus, A is more dispersed.

If the generalized variance is negative you have made a mistake somewhere in your calculation since the covariance matrix has to be positive semi-definite