CONTROLLABILITY AND THE LINEAR-EQUATION AX=B
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The linear equation Ax=b, with A nn, is considered, and it is shown that the controllable subspace of (A, b) can intersect the solution set of this equation in at most one point. Some additional properties of the controllable subspace related to the solution set are presented, and the role of controllability in establishing nonsingularity of A is exhibited. 1981.