"Linear Algebra with Applications" is a free and comprehensive textbook that introduces the computational, theoretical, and applied aspects of linear algebra.
The book covers topics such as systems of linear equations, matrices, determinants, vector spaces, linear transformations, eigenvalues and eigenvectors, diagonalization, inner product spaces, orthogonality, and many more. The explanations are accompanied by over 330 worked examples, exercises, and practical applications in geometry, electrical networks, dynamic systems, probability theory, and optimization.
A particularly interesting section discusses how Google's PageRank algorithm uses the dominant eigenvector to rank web pages. The links between websites are represented as a connectivity matrix, and the components of its dominant eigenvector provide an estimate of the relative importance of each page.
This is a very clear example of how an apparently abstract idea from linear algebra can underlie a real-world technology used on a massive scale.
The 2023 edition is available under a Creative Commons license. This is another excellent resource that is worth keeping as a reference.
https://collection.bccampus.ca/textbook/qTj4b4Ey
