LU Decomposition Visualizer
Interactive Step-by-Step Numerical Linear Algebra Pedagogical Tool
An interactive Next.js and TypeScript educational web application that visualizes step-by-step Gaussian row elimination and LU matrix factorization (PA = LU) for 2×2 to 5×5 matrices.
The Technical Bottleneck
Students learning numerical linear algebra often struggle to trace how elementary row operations accumulate into the lower-triangular multiplier matrix L and upper-triangular matrix U.
Why Existing Baselines Fail
Making matrix factorization states inspectable step-by-step turns an opaque algebraic routine into an intuitive visual algorithm.
Core Formulation & Insight
Built a client-side numerical linear algebra engine in TypeScript paired with a responsive Next.js / React / Tailwind / shadcn-ui interface that records every pivot, row operation, and intermediate L and U matrix state.
Architectural Design
Deterministic step-recording LU factorization engine with interactive playback controls.
1. Matrix Input & Dimension Controller (2×2 to 5×5)
Supports custom matrix entry, preset examples, and dimension switching.
2. Step-Recording Gaussian Elimination Engine
Computes exact row-reduction multipliers and snapshots intermediate L and U matrices at every elimination step.
3. Interactive Step Inspector & Theme Toggle
Highlights active pivot rows and multiplier entries with forward/backward step navigation.
Technical Stack & Systems Engineering
Implementation Highlights
- →Zero-latency client-side matrix factorization with clear mathematical state highlighting and dark/light theme support.
Datasets & Protocol
Datasets & Corpora
- 2×2 to 5×5 Dense Linear Algebra Test Matrices
Evaluation Protocol
Verified numerical factorization accuracy (L · U = A) across matrix dimensions.
Tracked Evaluation Metrics
Deployed an interactive linear algebra learning tool used to inspect step-by-step LU matrix transformations.
Full step-by-step L and U state inspection
Empirical Analysis & Interpretation
Bridges mathematical rigor (9.3/10 Linear Algebra coursework foundation) with clean TypeScript/Next.js interface engineering.
What This System Contributes
- 01Designed and implemented the numerical LU step engine and Next.js visualization UI.
Boundary Conditions & Future Work
- ·Scoped to 2×2–5×5 pedagogical matrices for screen readability.