Algebraic properties of the rank-deficient equality-constrained and weighted least squares problems (Q1183146)

The equality constrained least squares problem (LSE) is to minimize \(\| Kf-g\|_ 2\) over the set of \(f\) such that \(\| h-Lf\|_ 2\) is the minimum over all \(z\) of \(\| h-Lz\|_ 2\). The algebraic properties of the solutions of LSE and the corresponding weighted least squares problem (WLS) are studied. General solution formulas are given. It is not assumed that \(L\) and the block matrix \([L^ T,K^ T]^ T\) have full rank.