Axler - Linear Algebra Done Right



Springer UTM, 1996

Linear Algebra

"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 Spaces=

=Chapter 2 : Finite-Dimensional Vector Spaces=

=Chapter 3 : Linear Maps=

=Chapter 4 : Polynomials=

=Chapter 5 : Eigenvalues and Eigenvectors=

Upper-Triangular Matrices

 * "W invariant under T" means that $$TW \subseteq W$$.

Exercises
=Chapter 6 : Inner-Product Spaces=

=Chapter 7 : Operators on Inner-Product Spaces=

=Chapter 8 : Operators on Complex Vector Spaces=

=Chapter 9 : Operations on Real Vector Spaces=

=Chapter 10 : Trace and Determinant=