Tight infinite matrices

01/24/2023

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by   Ron Aharoni, et al.

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We give a simple proof of a recent result of Gollin and Joó: if a possibly infinite system of homogeneous linear equations Ax⃗ = 0⃗, where A = (a_i, j) is an I × J matrix, has only the trivial solution, then there exists an injection ϕ: J → I, such that a_ϕ(j), j≠ 0 for all j ∈ J.