Invariance of Numerical Character of Matrix Products and Their Statistical Applications

To study the invariance of numerical character of matrix products and their statistical applications by matrix theory and linear model theory. Necessary and sufficient conditions are established for the product AB -C to have its numerical characters invariant with respect to every minimum norm g inverse, respectively. The algebraic results derived are then applied to investigate relationships among BLUE, WLSE and OLSE under the general Gauss? Markoff model.