Jules <julianro...@gmail.com>

Suppose we have a doubly-indexed sequence {b_(i, j)} of real numbers,
with i, j positive integers.  Suppose also that we have a sequence
{c_i} of reals.  We wish to find a sequence {a_j} of reals so that the
sum as j goes from 1 to infinity of b_(i, j) * a_j = c_i for each i.
This is, in some sense, a collection of countably-many linear equations
in countably-many variables.  Are there any conditions on the
coefficients b_(i, j) that would guarantee existence and/or uniqueness
of a solution {a_j}?  If there were only finitely-many equations and
variables (the same number of each), then one could simply check that
the determinant of the coefficient matrix is non-zero.  Is there any
analog of determinant for an "omega-by-omega" matrix?