Unit 16: Abstract vector spaces
About this unit
A vector space is any collection you can add and scale by the usual rules, so polynomials and functions are vectors too, and maps like the derivative are linear maps with matrices and eigenvectors.
By the end, you can: Recognise a vector space from its addition and scaling rules, treat polynomials as vectors, and write the derivative as a matrix.
Modules
4 modulesLearn
- What made them vectorsArticle · Anything you can add and scale by the usual rules is a vector space: polynomials, functions and sound clips as well as arrows and lists.Not started
- Linear maps on functionsArticle · The derivative is a linear map; on polynomials of degree at most 3 it is a 4×4 matrix, and exponentials are its eigenvectors.Not started
- The whole module, in generalReview · The vector-space rules and how span, basis, linear maps, null space and eigenvectors carry over.Not started