Linear Algebra 1: Vectors, Span, Independence and Bases — A Visual Lesson | GroundUp Lab

Linear Algebra 1 — Vectors, span, independence and bases Given some arrows, where can you get to? Starting from a craft with two controls, this lesson builds the core ideas of linear algebra — vectors, linear combinations, span, linear independence, bases and coordinates, dimension, subspaces and direct sums, affine sets, matrices as column combinations, inner products, and conditioning — introducing every idea through a picture or analogy and then making it precise. 📖 Read this chapter (full proofs, worked examples, exercises and in-browser labs): https://lab.groundup.workers.dev/theory/#0... 🧪 GroundUp Lab — machine learning math, built from the ground up: https://lab.groundup.workers.dev Subscribe for the next chapter:    / @grounduplab-ai   Chapters 0:00 Where can you get to? 1:19 Act 1 · Moves and recipes 7:33 Act 2 · Reachable territory (span) 12:39 Act 3 · Dead weight (independence) 18:49 Act 4 · Addresses (basis and coordinates) 24:17 Act 5 · Seats (the exchange lemma and dimension) 30:28 Act 6 · Vectors that aren't arrows 36:23 Act 7 · Worlds inside worlds (subspaces, sums, affine sets) 43:26 Act 8 · Machines made of arrows (matrices) 49:01 Act 9 · Adding geometry (inner products) 58:19 Act 10 · Fragile addresses (conditioning) 1:04:29 Reachable? Unique? Stable? #linearalgebra #machinelearning #math