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?



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?

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    $\begingroup$ See this answer for a comparison of the trace and determinant of the covariance matrix as two measures for total variance. $\endgroup$
    – caracal
    Commented Aug 7, 2014 at 7:02

1 Answer 1


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


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