Springer UTM, 1996
"You are probably about to begin your second exposure to linear algebra. Unlike your first brush with the subject, which probably emphasized Euclidean spaces and matrices, we will focus on abstract vector spaces and linear maps. These terms will be defined later, so don't worry if you don't know what they mean. This books starts from the beginning of the subject, assuming no knowledge of linear algebra. The key point is that you are about to immerse yourself in serious mathematics, with an emphasis on you attaining a deep understanding of the definitions, theorems, and proofs."
Chapter 1 : Vector SpacesEdit
Chapter 2 : Finite-Dimensional Vector SpacesEdit
Chapter 3 : Linear MapsEdit
Chapter 4 : PolynomialsEdit
Chapter 5 : Eigenvalues and EigenvectorsEdit
Polynomials Applied to OperatorsEdit
- "W invariant under T" means that $ TW \subseteq W $.