Journal

Tag: span

Long-form notes, Qiskit experiments, and applied optimization thinking.

September 25, 2026•Learning Notes•5 min read

Why Linear Dependence Is Tested With Zero: Redundancy, Span, and the Nullspace

Why linear dependence is tested by a nontrivial combination equaling zero, why arbitrary coefficients do not produce every vector, how span limits what can be produced, and how dependence connects directly to the nullspace.

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September 15, 2026•Learning Notes•4 min read

From a Reduced Matrix to the Nullspace: Free Variables, Special Solutions, and Span

How row reduction exposes free variables, how free variables produce special solutions, and why the entire nullspace is the span of those special solutions.

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