Unit 5: Three-dimensional linear transformations
About this unit
A linear map of 3D space is fixed by where î, ĵ and k̂ land; a 3×3 matrix records those three images as its columns, applies to (x, y, z) as x, y and z copies of them, and composes right to left just like a 2×2 matrix.
By the end, you can: Read a 3×3 matrix as where î, ĵ and k̂ land, apply it to a 3D vector, recognise standard motions of space and compose them.
Modules
4 modulesLearn
- Three arrows decide everythingArticle · A linear map of space is fixed by where î, ĵ and k̂ land; a 3×3 matrix lists those three images as columns, and Mv = x·(first column) + y·(second) + z·(third).Not started
- Four motions of space, and chaining themArticle · Rotation about the z-axis, scaling, a shear and projection onto a plane, each read from its columns; composing 3×3 matrices works exactly like 2×2, right to left, column by column.Not started
- Space in three columnsReview · What a 3×3 matrix is, how to apply it, the standard examples and how products work.Not started