Session 1 - Linear Algebra I

Everything in linear algebra built from two operations, adding and scaling vectors, up to the matrix as a transformation of space.

Topics covered

• Vectors, linear combinations, span, and linear independence
• The dot product: norm, angle, and cosine similarity
• Projection: the shadow and the residual
• Orthonormal bases and change of basis
• Matrices as transformations; the columns as where the axes land
• The data matrix, and applying a scoring rule to everyone at once

Materials

• 📊 Slides
• ✏️ Exercise sheet
• ✅ Solutions