Linear Algebra


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.