A theorem on the extension of a rectangular matrix of continuous functions to become a nonsingular square matrix
H.F. Mathis · Proceedings of the American Mathematical Society · 1950
has maximum rank everywhere on K. At any point u on K at least one of the p Xp determinants of the matrix B is different from zero in a neighborhood of u. Consequently the cube K can be divided into a finite number of cubes ka, the length of whose edges are equal and whose edges are parallel to the n coordinate axes, so that for each cube ka at least one p Xp determinant of the matrix B does not vanish on the closed cube ka. If the proper q-p /3's are arbitrarily chosen on one of the cubes ka so that they are continuous, the remaining fl's will be uniquely determined and con-