This paper presents some theorems for real matrices which should be of use and interest to anyone working with quadratic forms in normally distributed variables because of the following equivalences: ...

In this paper, we first establish a series of closed-form formulas for calculating the extremal ranks and inertias of f (X) subject to X ∈ Ω by applying the generalized inverses of matrices.

Without loss of generality, we assume that the quadratic form is normalized such that matrix H is symmetric, the neutral stimulus (usually an average or blank stimulus) is zero, and the response ...