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Newsgroups: sci.math
From: "Jules" <julianro...@gmail.com>
Date: 12 Nov 2006 22:12:39 -0800
Local: Mon, Nov 13 2006 5:12 pm
Subject: Infinite system of linear equations
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? You must Sign in before you can post messages.
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