PPolySim OS

SVD

The factorization behind image compression, PCA, and recommender systems — made visible. Reconstruct a 64×64 image from just its top k singular values.

SVD StudioLive

Controls

A real one-sided Jacobi SVD factors a 64×64 image into modes A = UΣVᵀ. Keep the top k singular values to compress it — watch the shape emerge as k grows.

Presets

▶ Run in Python

Data Inspector

Rank k6 / 64
Energy captured100.0%
Compression5.3×
Stored numbers774

Governing equation

Reading this result: Rank 6 already reconstructs 100.0% of the energy: the result is visually indistinguishable from the original, yet stores about 5.3× fewer numbers.

Runs locally in your browser — free forever. Scale to the cloud when reality gets heavy.

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How it works

Singular value decomposition factors any matrix as A = UΣVᵀ, ordering the data's structure from strongest to weakest. This studio runs a real one-sided Jacobi SVD in your browser, then reconstructs the image from only the top k modes (A_k = Σσᵢuᵢvᵢᵀ). A handful of singular values captures most of the image's energy — the same low-rank idea powers JPEG-style compression, principal component analysis, and latent-factor recommender systems.

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The math, the assumptions, real-world uses, or a code translation — explained for this exact simulation.

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Frequently asked questions

Is this singular value decomposition tool really free?
Yes. SVD runs entirely in your browser using your device's own compute, so local use is free forever. You only pay Compute Tokens if you scale a job to the cloud.
Do I need to install anything?
No. Everything runs client-side in a modern browser — no downloads, no license, no account required to start.
Can I save or share my simulation?
Create a free account to save projects, and use a shareable embed or minted DOI to publish a live, interactive version anywhere.
How accurate are the results?
The solver uses established numerical methods, but results are for research and educational purposes and should be validated against experiment or professional review before you rely on them.