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An <em>m</em> by <em>n</em> matrix <em>A</em> has <em>n</em> columns each in <strong>R</strong><sup>m</sup>. Capturing all combinations Av of these columns gives the column space – a subspace of <strong>R</strong><em><sup>m</sup></em>.
Differential Equations and Linear Algebra, 5.1: The Column Space of a Matrix, A - MATLAB & Simulink