Any covariance matrix $A$ must be non-negative definite or semi-positive definite. This means that its deteraminant should always $|A|\ge0$. In case $|A|=0$, what would happen? or what does this mean for the dependence of the corresponding random variables?

Million thanks for your answers and hints


marked as duplicate by whuber Jun 3 '14 at 13:31

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  • $\begingroup$ There's a linear combination of variables which is constant. $\endgroup$ – Glen_b Jun 3 '14 at 13:24
  • $\begingroup$ For example this answer covers it. $\endgroup$ – ttnphns Jun 3 '14 at 13:29