The Drazin Inverse of an Infinite Matrix
Stephen L. Campbell · SIAM Journal on Applied Mathematics · 1976
Let $A = [ {a_{ij} } ]$, $0\leqq i < \infty $, $0\leqq j < \infty $. Then A is called a denumerably infinite matrix. A way to define a Drazin inverse for A is presented. The application of this definition to denumerable Markov chains, infinite linear systems of differential equations, and linear operators on Banach spaces is discussed.