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Newsgroups: sci.math
From: Gottfried Helms <he...@uni-kassel.de>
Date: Mon, 13 Nov 2006 07:30:44 +0100
Local: Mon, Nov 13 2006 5:30 pm
Subject: Re: Infinite system of linear equations
Am 13.11.2006 07:12 schrieb Jules:
> Suppose we have a doubly-indexed sequence {b_(i, j)} of real numbers, Just an idea: > 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? I actually don't know; what comes to mind is: - either the matrix is triangularizable by noniterative Then the determinant is the limit of the product of the But I think this implies strict conditions for your Gottfried Helms You must Sign in before you can post messages.
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