Unit 3: Linear transformations and matrices
About this unit
A linear transformation keeps the origin fixed and grid lines straight, parallel and evenly spaced, so it is fixed by where î and ĵ go; a matrix records those two images as its columns.
By the end, you can: See a linear transformation as a motion of the whole plane, read a 2×2 matrix as where î and ĵ go, and multiply a matrix by a vector.
Modules
5 modulesLearn
- Moving the whole planeArticle · A transformation moves every vector at once; it is linear when the origin stays put and grid lines stay straight, parallel and evenly spaced.Not started
- A matrix is two columnsArticle · A linear map is fixed by where î and ĵ go; a 2×2 matrix records those two images as columns, and Av = x·(first column) + y·(second column).Not started
- Watch the grid moveExperiment · Step through a matrix acting on the plane and see each output built from the columns.Not started
- Maps, columns, productsReview · Linearity, the column picture of a matrix and the matrix–vector product.Not started