An infinite matrix is a doubly indexed array 
having infinitely many rows or columns. It defines
a linear transformation on a sequence space
only when the associated series converge and the resulting sequence remains in the
space. Bounded operators on 
admit infinite matrix representations relative to an orthonormal
basis.
Infinite Matrix
See also
Matrix, OperatorExplore with Wolfram|Alpha
References
Cooke, R. G. Infinite Matrices and Sequence Spaces. London, England: Macmillan, 1950.Cite this as:
Weisstein, Eric W. "Infinite Matrix." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/InfiniteMatrix.html