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Linear Algebra Linear Algebra by Lang

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  1. Jan 24, 2013 #1

    micromass

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    Staff Emeritus
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    Education Advisor
    2016 Award


    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
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  3. Feb 1, 2013 #2

    phion

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    Gold Member

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