Linear Algebra Lab

Drag vectors to see a span collapse, warp the grid with a matrix, hunt eigenvectors by hand, run Gram–Schmidt step by step, and watch a circle become an ellipse under the SVD.

What you can try

• Rank and null space
• Eigenvectors
• Singular value decomposition

• Transformer Lab — Tokenize with BPE, watch attention heads, rotate positions with RoPE, size a KV cache, route tokens to experts and quantize weights.
• RAG Lab — Chunk a handbook, search it by meaning, fuse BM25 with dense retrieval, rerank, measure recall and NDCG, and keep the index fresh.
• Machine Learning Lab — Find principal components, run k-means and EM step by step, tame overfitting with ridge and lasso, and compare kNN, trees, naive Bayes, SVMs and boosting.
• Deep Learning Lab — Build neural networks from scratch. Explore 3D error surfaces, optimizers, backpropagation, overfitting and convolutions.
• Image Processing Lab — Sampling, filtering, Fourier transforms, segmentation, SIFT and HOG, applied to a live image you can change.
• All simulators