Linear algebra book written by Peter Petersen published by Springer Publisher.
This book takes a different approach in presenting linear algebra. It has five long chapter with lots of sections. Explains using geometric drawings.
Chapter 1.13 does Gaussian elimination.
Chapter 2 is on Linear Operations. Covers linear differential equations. Eigenvalues including a definition of the German word eigen. Uses Gaussian elimination instead of determinants to find eigenvalues.
2.5 shows diagonalizability with Fibonacci Sequence as an example.
Chapter 3 is on inner product spaces. Including Quaternions, Cauchy-Schwarz, Triangle Inequality, OR Factorization, and Matrix Exponentials.
Chapter 4 covers Linear Operations on Inner Products. Including Polarization and Isometrics,. 4.3 is about Spectral Theorem.
4.9 Singular Value Decomposition.
Chapter 5 is on determinants. Using a geometric approach then an Algebraic approach. Then uses the theory applied to the study of linear differential equations.