Journal
Long-form notes, Qiskit experiments, and applied optimization thinking.
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.
Read note →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.
Read note →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 →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 →