Variance of a random vector (different of the covariance matrix) Tipically, the variance of a p-dimensional random vector
$$X = (X_1,...,X_p)$$
is defined as a the covariance matrix given by:
$$E[ (X- EX)^T(X- EX)  ]$$
But, in the second page of this paper, the variance of $X$ is defined as:
$$v(X)= E|X - EX|^2$$
I've never seen this definition and I would like to know more about this definition.
Some help?

First of all, this $v(X)$ is the sum $\sum_i Var(X_i),$ so $v(X)$ is just the trace of the covariance matrix. I think that mathematically $v(X)$ makes a lot of sense and it is basically a measure of how much $X$ is different from a constant random vector. Of course, we could also consider other analogues quantities like the determinant of the covariance matrix or its norm, etc.
