I'm well aware on this question on Generalized Variance that says that
Generalized variance is the determinant of covariance matrix.
So it would be:
$$\operatorname{var}_G(\matrix{A}) = \operatorname{det}\operatorname{Cov}(\matrix{A})$$
On Wikipedia however, it says:
Another natural generalization of variance for such vector-valued random variables $\matrix{X}$, which results in a scalar value rather than in a matrix, is obtained by interpreting the deviation between the random variable and its mean as the Euclidean distance. This results in $\operatorname{E} \left[(X-\mu)^{\operatorname{T}}(X-\mu )\right]=\operatorname{tr}(C)$, which is the trace of the covariance matrix.
So it would be the sum of the variances of the single vectors in the covariance matrix:
$$\operatorname{var}_G(\matrix{A}) = \operatorname{tr}\operatorname{Cov}(\matrix{A})$$
I'm failing to find a publication defining it on Google Scholar, so I'm asking here how is the generalized sample variance defined?
Thanks!