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
low-rank image compression
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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.
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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Ask the AI about this model
The math, the assumptions, real-world uses, or a code translation — explained for this exact simulation.
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.