Journal

Tag: linear-algebra

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

August 29, 2026•Learning Notes•5 min read

Understanding A = LU: How LU Factorization Was Already Hiding Inside Gaussian Elimination

LU factorization initially looks like a new idea introduced after Gaussian elimination. But if elimination already gives EA = U, then A = E^{-1}U. This note follows that question step by step and shows how L naturally emerges by saving the elimination multipliers.

Read note →

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.

Read note →