From Zhav Loizeau in #1:
I cannot not comment on “random” form because I reaaaaally wish it were either “un-correlated”, “independent” (this is not quite true as one can define un-correlated random variables that are dependent e.g., Image), or “diagonal” (to describe the shape of the matrix).
Still no standard in sight. As mentioned before, there is a Wikipedia page (why not).