Learning resources

Books

Linear algebra: the theory of vector spaces and linear transformations. This is a free, open-source text designed for a first course in linear algebra and authored using PreTeXt.

This treatment of linear algebra introduces abstract vector spaces early on, as the chapter overview below indicates. However, matrices and Euclidean spaces make up a large portion of the examples and exercises, and it is possible to design a matrix-focused course using the text.

  • Chapter 0: foundations. Sets and functions, logic and proof technique, polynomials and complex numbers.
  • Chapter 1: systems of linear equations. Solving systems of linear equations with Gaussian elimination.
  • Chapter 2: matrices. Matrix arithmetic and algebra. Invertible matrices. Determinant.
  • Chapter 3: vector spaces and linear transformations. Vector spaces, linear transformations, subspaces, span and linear independence, basis, dimension, rank-nullity.
  • Chapter 4: inner product spaces. Inner products, orthogonality, orthogonal projections.
  • Chapter 5: eigenvectors and diagonalization. Matrix representations of linear transformations, change of basis, eigenvectors, diagonalization, the spectral theorem.

Kursobjekte {#kursobjekte}

Enamored of compound nouns, and susceptible to fits of pretension, I’ve chosen ‘Kursobjekt’ (German for “course object”) to describe the course tools you find below. These are hybrid creatures: book-like, but more terse; official records of course content, and hence useful as review tools; enhanced with interactive and computational cells; created on the fly while teaching, and with a “quick and dirty” ethos. The Kursobjekte are free and open source, authored using PreTeXt.