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?

In the first page, they define $|x|=\sqrt{x'x}$, which yields
$$v(X)=E[(X-E[X])^T(E-E[X])]$$
which seems like it's same as yours; but it's not, because the paper uses its own variance definition and vector dimensions.
