Unit 4: Matrix multiplication as composition
About this unit
Applying B and then A is one linear map with matrix AB, read right to left; each column of AB is A applied to the matching column of B, and the order of the factors matters.
By the end, you can: Treat a matrix product as doing one transformation after another, compute it column by column, and know why the order matters.
Modules
5 modulesLearn
- One map after anotherArticle · Doing one linear map and then another is again linear, so it has a matrix, the product; read it right to left and find it by tracking î and ĵ.Not started
- A product, column by columnWalkthrough · Compute a 2×2 product by sending each column of the right matrix through the left one, then check with rows times columns.Not started
- Shear then turn, or turn then shearWalkthrough · Multiply a rotation and a shear in both orders and see the results differ; associativity holds because both groupings mean the same sequence.Not started
- Multiplying as composingReview · What a product means, how to compute it, and the rules it does and doesn't follow.Not started