Journal
Long-form notes, Qiskit experiments, and applied optimization thinking.
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.
Read note →How row reduction exposes free variables, how free variables produce special solutions, and why the entire nullspace is the span of those special solutions.
Read note →A question-driven explanation of nullspace and linear independence, moving beyond Ax = 0 to the mental pictures of redundant vectors and input changes that a matrix cannot detect.
Read note →