Journal

Tag: ax-b

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

August 30, 2026•Learning Notes•6 min read

Why LU Matters for Large Systems: From Ax = b to Pivoting and PA = LU

Gaussian elimination is easy to demonstrate on small matrices, but real systems may contain thousands or millions of unknowns. This note follows the question of how computers solve large Ax = b systems, why LU makes repeated solutions efficient, and why zero or tiny pivots lead naturally to row exchanges and PA = LU.

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August 27, 2026•Learning Notes•5 min read

Why Matrices Matter – From Real World Rules to Ax = b, Inverses and Elimination

Matrices become much easier to understand when we stop seeing them as boxes of numbers and start seeing them as rules or actions. This note builds that intuition from a simple production example and shows why Ax = b, inverse matrices and Gaussian elimination naturally follow.

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