On the unilateral equation in matrices
William E. Roth · Transactions of the American Mathematical Society · 1930
The equation (1) ÍLaíX*-í = 0, in which the coefficients A{, i = 0, 1, 2, ■ ■ ■ , p, are mXn matrices having m rows and n columns of scalar elements, and where X is an »X» matrix, is said to be unilateral! in that the known matrices Ai, i = 0, 1, 2, ■ ■ ■ , p, occur as factors on the left (or on the right) of each term of its left member.In case m = n the equation was studied by Sylvester in several papers of a series that appeared largely in the Johns Hopkins University Circulars of 1883 and 1884, the Philosophical Magazine, and the Comptes Rendus de l'Académie de Sciences.4;The solution of particular types of equations in matrices that may be regarded as special cases under the above was further studied by Buchheim, Frobenius, Taber, Kreis, Cecioni, Wedderburn and others.§ The restrictions adopted heretofore were such that the given