Journal

Tag: rank

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

October 1, 2026•Learning Notes•4 min read

How a Parameter Changes Rank: Pivot Variables, Free Variables, and Special Solutions

A step-by-step study of Strang's parameter-dependent rank example, showing how pivots identify pivot variables, why nonpivot variables are free, and why c=4 causes the rank to drop and the nullspace to gain an extra direction.

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September 30, 2026•Learning Notes•4 min read

Understanding Rank and Rank-One Matrices: Pivots, Redundancy, and Nullspace Geometry

An intuitive study of matrix rank, why pivots measure independent information, how special nullspace solutions expose redundant columns, and why rank-one matrices have the form A=uv^T.

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