Minimization of quadratic forms using the Drazin-inverse solution - Stanimirović, Predrag S.; Pappas, Dimitrios; Miljković, Sladjana (Linear & multilinear algebra, 2014)
We analyse the problem of constrained minimization of the real quadratic functional , subject to the inconsistent system of linear equations , where is a positive definite or positive semidefinite matrix. Both cases are analysed separately, and respective relationships have been established between the solution of the original problem and the Drazin-inverse solution of the equation . In the special case when is a positive definite and , we show that the solution of the problem can be represented as a particular -inverse solution.