Lab Overview

Interactive and computational labs for Linear Algebra as a Language. Each chapter has a Jupyter notebook for deeper Python work and a standalone HTML lab for visual exploration.

View all labsHow to use the labs

How to use these labs

Recommended rhythm: read the chapter story, explore the interactive page, then work through the notebook. The HTML labs build intuition; the notebooks turn intuition into computation.
1. RepresentationChapters 1–4 turn the world into vectors, tables, and data clouds.
2. TransformationChapters 5–8 use matrices as machines and study solving, rank, and information loss.
3. GeometryChapters 9–12 develop distance, angle, projection, and orthogonality.
4. Hidden structureChapters 13–18 reveal eigenvectors, energy, SVD, compression, and PCA.
5. Signals and AIChapters 19–25 connect Fourier, Haar, images, text, neural networks, recommendation, and AI.

Lab cards

02

Vectors: Numbers with Meaning

Vectors as points, arrows, states, and high-dimensional objects

Google Colab Interactive
06

Stretching, Rotating, Shearing

Geometric transformations, determinant, area, and composition

Google Colab Interactive
09

Length and Distance

Norms, distances, nearest neighbors, and high-dimensional distance

Google Colab Interactive
10

Angles and Similarity

Dot products, cosine similarity, correlation, and text similarity

Google Colab Interactive
14

Stability, Ranking, Iteration

Power iteration, Markov chains, stationary behavior, and ranking

Google Colab Interactive
15

Energy Landscapes

Quadratic forms, positive definiteness, gradients, and optimization

Google Colab Interactive
16

SVD: Matrix Microscope

Singular values, rank-one layers, low-rank structure, and denoising

Google Colab Interactive
19

Fourier Analysis

Signals as vectors, frequency bases, FFT, filtering, and compression

Google Colab Interactive
20

Haar Wavelets

Local averages, differences, multiscale structure, compression, and denoising

Google Colab Interactive
21

Images as Matrices

Pixels, color channels, convolution, edges, pooling, and feature maps

Google Colab Interactive
23

Neural Networks as Matrix Machines

Layers, activations, softmax, hidden representations, and training

Google Colab Interactive
24

Recommendation Systems

User-item matrices, similarity, latent factors, and matrix factorization

Google Colab Interactive
25

The Grammar of AI

Embeddings, attention, neural layers, vector search, and AI systems

Google Colab Interactive

Complete lab list

ChapterLabMain ideaGoogle ColabInteractive
1The World as NumbersRepresentation, features, scaling, and first data geometryGoogle ColabInteractive
2Vectors: Numbers with MeaningVectors as points, arrows, states, and high-dimensional objectsGoogle ColabInteractive
3Combining IdeasLinear combinations, span, mixtures, and matrix-vector productsGoogle ColabInteractive
4Data as PointsData clouds, features, scaling, clusters, and nearest neighborsGoogle ColabInteractive
5Matrix MachinesMatrices as transformations and feature-mixing machinesGoogle ColabInteractive
6Stretching, Rotating, ShearingGeometric transformations, determinant, area, and compositionGoogle ColabInteractive
7Solving BackwardsLinear systems, inverse problems, elimination, and consistencyGoogle ColabInteractive
8When Information Is LostRank, null space, column space, and information lossGoogle ColabInteractive
9Length and DistanceNorms, distances, nearest neighbors, and high-dimensional distanceGoogle ColabInteractive
10Angles and SimilarityDot products, cosine similarity, correlation, and text similarityGoogle ColabInteractive
11Projection: The Best ShadowProjection, residuals, least squares, and approximationGoogle ColabInteractive
12OrthogonalityOrthonormal bases, Gram-Schmidt, QR, and stable computationGoogle ColabInteractive
13EigenvectorsHidden directions, eigenvalues, repeated action, and data variationGoogle ColabInteractive
14Stability, Ranking, IterationPower iteration, Markov chains, stationary behavior, and rankingGoogle ColabInteractive
15Energy LandscapesQuadratic forms, positive definiteness, gradients, and optimizationGoogle ColabInteractive
16SVD: Matrix MicroscopeSingular values, rank-one layers, low-rank structure, and denoisingGoogle ColabInteractive
17Image CompressionImages, SVD compression, storage, energy, and denoisingGoogle ColabInteractive
18PCAVariance, covariance, scores, loadings, dimension reduction, and visualizationGoogle ColabInteractive
19Fourier AnalysisSignals as vectors, frequency bases, FFT, filtering, and compressionGoogle ColabInteractive
20Haar WaveletsLocal averages, differences, multiscale structure, compression, and denoisingGoogle ColabInteractive
21Images as MatricesPixels, color channels, convolution, edges, pooling, and feature mapsGoogle ColabInteractive
22Text as VectorsDocument vectors, TF-IDF, cosine search, SVD topics, and embeddingsGoogle ColabInteractive
23Neural Networks as Matrix MachinesLayers, activations, softmax, hidden representations, and trainingGoogle ColabInteractive
24Recommendation SystemsUser-item matrices, similarity, latent factors, and matrix factorizationGoogle ColabInteractive
25The Grammar of AIEmbeddings, attention, neural layers, vector search, and AI systemsGoogle ColabInteractive

Suggested assignment patterns

Short weekly labComplete selected notebook cells plus one reflection question.
Interactive pre-classExplore the HTML page and write three observations before lecture.
Full computational labComplete the full notebook, including student tasks and extensions.
Mini-project extensionModify a dataset, image, signal, text corpus, or network from the lab.