Let be given by:
We need to show that C is smaller than unity in some norm. Therefore, we calculate:
Thus, we know from the statement above that exists.
The Neumann series has been used for linear data detection in massive multiuser multiple-input multiple-output (MIMO) wireless systems. Using a truncated Neumann series avoids computation of an explicit matrix inverse, which reduces the complexity of linear data detection from cubic to square.[1]
Another application is the theory of Propagation graphs which takes advantage of Neumann series to derive closed form expression for the transfer function.
- Werner, Dirk (2005). Funktionalanalysis (in German). Springer Verlag. ISBN 3-540-43586-7.