Expressions for Generalized Inverses of a Bordered Matrix with Application to the Theory of Constrained Linear Models
Rose M. Pringle, Arthur A. Rayner · SIAM Review · 1970
Expressions for generalized inverses of a well-known bordered matrix are derived. These expressions find application in the solution of systems of linear equations obtained by using Lagrange multipliers to find a constrained minimum. In particular, they are used to obtain explicit representations for minimum variance linear unbiased estimates of estimable linear functions in the linear model with restricted parameters.