Journal

Tag: pivot-variables

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

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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September 13, 2026•Learning Notes•5 min read

Finding the Nullspace Step by Step: From Ax = 0 to Free Variables and Special Solutions

A step-by-step study of Strang Chapter 3 Section 3.2 showing how elimination reveals redundant equations, free variables, special solutions, and finally the complete nullspace.

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