Inverses of matrices and matrix-transformations
Albert Wilansky, Karl Zeller · Proceedings of the American Mathematical Society · 1955
Let A = (a"k), n,k = l,2, • ■ ■ , be a matrix of complex numbers.Let D be the set (linear sequence space) of sequences x= {xn\ such that y=Ax is defined; y being the sequence {yn}, where yn= 2* ankXk for each n.Let R be the set of all ^4x, xED.We call D and R the domain and range of A. They are linear subspaces of (s), the space of all sequences.To emphasize the distinction between inverse matrix and inverse transformation, we denote Ax by T(x), thus defining T:D-*R, and investigate, under various hypotheses:(a) the existence of right, left, and two-sided inverses for A, de-