Linear algebra as an introduction to abstract mathematics

What is linear algebra?

Introduction to complex numbers

The fundamental theorem of algebra and factoring polynomials

Vector spaces

Span and bases

Linear maps

Eigenvalues and Eigenvectors

Permutations and the determinant of a square matrix

Inner product spaces

Change of bases

The spectral theorem for normal linear maps

Appendix A. Supplementary notes on matrices and linear systems

Appendix B. The language of sets and functions

Appendix C. Summary of algebraic structures encountered

Appendix D. Some common math symbols and abbreviations.