THE MATRIX EQUATION AX-YB=C AND RELATED PROBLEMS

摘要

The main result of the paper is a theorem, using which a new proof of Roth's theorem is obtained, a new solvability criterion for the matrix equation AX - YB = C is proved, a formula for a particular solution of the latter is derived, and the least of the orders of square nonsingular matrices containing a given rectangular matrix as a submatrix is determined. Bibliography: 5 titles.