Estimates of solutions for ambiguously solvable linear matrix equations

The article examines the problem of estimating solutions of operator equations under conditions of uncertainty. We obtain the expressions for guaranteed errors of solutions of indefinite linear equations in the spaces of rectangular matrices in the presence of additional data with deterministic errors belonging to special sets. In a particular case, explicit formulas are obtained for guaranteed linear vector estimates and guaranteed vector estimation errors and for guaranteed posterior estimates and measurement errors. These estimation results are illustrated by a test example in the case of operators that act in the space of 2×2 matrices with a non-zero kernel.