Journal

Tag: lu-factorization

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 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.

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