Linear Algebra Linear Algebra by Lang

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1. Jan 24, 2013

micromass

Table of Contents:
Code (Text):

[LIST]
[*] Basic Theory
[LIST]
[*] Vectors
[LIST]
[*] Definition of points in n-space
[*] Located vectors
[*] Scalar product
[*] The norm of a vector
[*] Lines and planes
[*] The cross product
[*] Complex numbers
[/LIST]
[*] Vector Space
[LIST]
[*] Definitions
[*] Bases
[*] Dimension of a vector space
[*] Sums and direct sums
[/LIST]
[*] Matrices
[LIST]
[*] The space of matrices
[*] Linear equations
[*] Multiplication of matrices
[*] Appendix. Elimination
[/LIST]
[*] Linear Mappings
[LIST]
[*] Mappings
[*] Linear mappings
[*] The kernel and image of a linear map
[*] Composition and inverse of linear mappings.
[*] Geometric applications
[/LIST]
[*] Linear Maps and Matrices
[LIST]
[*] The linear map associated with a matrix
[*] The matrix associated with a linear map
[*] Bases, matrices, and linear maps
[/LIST]
[*] Scalar Products and Orthogonality
[LIST]
[*] Scalar products
[*] Orthogonal bases, positive definite case
[*] Application to linear equations
[*] Bilinear maps and matrices
[*] General orthogonal bases
[*] The dual space
[/LIST]
[*] Determinants
[LIST]
[*] Determinants of order 2
[*] Existence of determinants
[*] Additional properties of determinants
[*] Cramer's rule
[*] Permutations
[*] Uniqueness
[*] Determinant of a transpose
[*] Determinant of a product
[*] Inverse of a matrix
[*] The rank of a matrix and subdeterminants
[*] Determinants as area and volume
[/LIST]
[/LIST]
[*] Structure Theorems
[LIST]
[*] Bilinear Forms and the Standard Operators
[LIST]
[*] Bilinear forms
[*] Quadratic forms
[*] Symmetric operators
[*] Hermitian operators
[*] Unitary operators
[*] Sylvester's theorem
[/LIST]
[*] Polynomials and Matrices
[LIST]
[*] Polynomials
[*] Polynomials of matrices and linear maps
[*] Eigenvectors and eigenvalues
[*] The characteristic polynomial
[/LIST]
[*] Triangulation of Matrices and Linear Maps
[LIST]
[*] Existence of triangulation
[*] Theorem of Hamilton-Cayley
[*] Diagonalization of unitary maps
[/LIST]
[*] Spectral Theorem
[LIST]
[*] Eigenvectors of symmetric linear maps
[*] The spectral theorem
[*] The complex case
[*] Unitary operators
[/LIST]
[*] Polynomials and Primary Decomposition
[LIST]
[*] The Euclidean algorithm
[*] Greatest common divisor
[*] Unique factorization
[*] The integers
[*] Application to the decomposition of a vector space
[*] Schur's lemma
[*] The Jordan normal form
[/LIST]
[/LIST]
[*] Relations with Other Structures
[LIST]
[*] Multilinear Products
[LIST]
[*] The tensor product
[*] Isomorphisms of tensor products
[*] Alternating products: Special case
[*] Alternating products: General case
[*] Appendix: The vector space generated by a set
[/LIST]
[*] Groups
[LIST]
[*] Groups and examples
[*] Simple properties of groups
[*] Cosets and normal subgroups
[*] Cyclic groups
[*] Free abelian groups
[/LIST]
[*] Rings
[LIST]
[*] Rings and ideals
[*] Homomorphisms
[*] Modules
[*] Factor modules
[/LIST]
[/LIST]
[*] Appendix: Convex Sets
[LIST]
[*]  Definitions
[*] Separating hyperplanes
[*] Extreme points and supporting hyperplanes
[*] The Krein-Milman theorem
[/LIST]
[*] Appendix: Odds and Ends
[LIST]
[*] Induction
[*] Algebraic closure of the complex numbers
[*] Equivalence relations
[/LIST]
[*] Appendix: Angles
[*] Answers
[*] Index
[/LIST]

Last edited by a moderator: May 6, 2017
2. Feb 1, 2013

phion

Last edited by a moderator: May 6, 2017
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