Unit 8: Nonsquare matrices as transformations between dimensions
About this unit
An m×n matrix is a linear map from n dimensions to m: its n columns are where the n input basis vectors land, each with m coordinates. A product AB makes sense only when B's outputs have as many entries as A's inputs.
By the end, you can: Read an m×n matrix as a map from n dimensions to m, apply it, and tell which products of matrices are defined.
Modules
4 modulesLearn
- From the plane into spaceArticle · A 3×2 matrix sends 2D inputs to 3D outputs: its columns are where î and ĵ land, and the outputs fill a plane through the origin.Not started
- Down a dimension, and chaining mapsArticle · A 2×3 matrix sends 3D to 2D and a 1×2 matrix sends the plane to the number line; columns count the input dimension, rows the output, and a product is defined when the dimensions in the middle match.Not started
- Reading a matrix's shapeReview · What the shape of a matrix says about the map it describes.Not started