Let $(a_{mn})_{m,n\in\mathbb{N}}$ and $(b_m)$ be sequences of complex numbers.We say that $(a_{mn})$ and $(b_m)$ constitute *an infinite system of linear equations in infinitely many variables* if we seek a sequence $(x_n)$ of complex numbers such that $\forall m\in\mathbb{N}:$ $\sum_{n=1}^{\infty}a_{mn}x_n=b_m$. Note that in general the order of summation matters.

I am sort of a undergraduate student with focus on number theory and have some background in functional analysis (2 semesters functional analysis, 1 semester non-linear functional analysis, 1 semester operator algebras, 2 semesters PDEs), so I am sort of a becoming number-theorist with bias for functional analysis :-) That is also why I am fascinated by the above defined object as a sort of natural extension of a practical problem from linear algebra.

We have never dealt with this type of objects and I wasn´t able to find much on google that I could start something with, maybe partly because I have searched in the wrong way. That is why I have a request if you could recommend some **introductory** literature *focused* on such infinite systems of linear equations in infinitely many unknowns over $\mathbb{C}$.

Thanks in advance!

stronglyfeel that MO should not be a place for questions of the form "tell mestuff" or "write me a Wikipedia/nLab entry" – Yemon Choi Aug 22 '10 at 2:26