Introduction to Linear Algebra by Lang

[micromass]

• Author: Serge Lang
• Title: Introduction to Linear Algebra
• Amazon Link: https://www.amazon.com/dp/3540780602/?tag=pfamazon01-20
• Prerequisities: High-School mathematics
• Level: Undergrad

Table of Contents:

[LIST]
[*] Vectors
[LIST]
[*] Definition of Points in Space
[*] Located Vectors
[*] Scalar Product
[*] The Norm of a Vector
[*] Parametric Lines
[*] Planes
[/LIST]
[*] Matrices and Linear Equations
[LIST]
[*] Matrices
[*] Multiplication of Matrices
[*] Homogeneous Linear Equations and Elimination
[*] Row Operations and Gauss Elimination
[*] Row Operations and Elementary Matrices
[*] Linear Combinations
[/LIST]
[*] Vector Spaces
[LIST]
[*]  Definitions
[*] Linear Combinations
[*]  Convex Sets
[*] Linear Independence
[*] Dimension
[*] The Rank of a Matrix
[/LIST]
[*] Linear Mappings
[LIST]
[*] Mappings
[*] Linear Mappings
[*] The Kernel and Image of a Linear Map
[*] The Rank and Linear Equations Again
[*] The Matrix Associated with a Linear Map
[*] Appendix: Change of Bases
[/LIST]
[*] Composition and Inverse Mappings
[LIST]
[*] Composition of Linear Maps
[*] Inverses
[/LIST]
[*] Scalar Products and Orthogonality
[LIST]
[*]  Scalar Products 
[*]  Orthogonal Bases 
[*]  Bilinear Maps and Matrices
[/LIST]
[*] Determinants
[LIST]
[*] Determinants of Order 2
[*] The Rank of a Matrix and Subdeterminants
[*] Cramer's Rule
[*] Inverse of a Matrix
[*] Determinants as Area and Volume
[/LIST]
[*] Eigenvectors and Eigenvalues 
[LIST]
[*] Eigenvectors and Eigenvalues
[*] The Characteristic Polynomial
[*] Eigenvalues and Eigenvectors of Symmetric Matrices
[*] Diagonalization of a Symmetric Linear Map
[/LIST]
[*] Appendix: Complex Numbers
[*] Answers to Exercises
[*] Index
[/LIST]

 

[mathwonk]

well again i am handicapped by prior familiarity with earlier versions of these books from 40 years ago. i was originally very impressed by his book because it had chapters entitled:

"the linear map associated to a matrix"

and " the matrix associated to a linear map>

only one of these seems to survive here, but i presume it is as clear as the earlier one.