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When we say a problem is an overdetermined system, what do we mean by that in a rigorous fashion?

Thanks.

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It means (in a linear system) that there are more equations than unknowns. As a consequence, there may be no solutions (the equations are inconsistent) or some equations are linear combinations of others.

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    Things are more complicated for polynomial systems. See the section "In general use" of that Wikipedia page.2016-11-15