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Main Question or Discussion Point
- Author: Kenneth Hoffman, Ray Kunze
- Title: Linear Algebra
- Amazon link https://www.amazon.com/dp/0135367972/?tag=pfamazon01-20
- Prerequisities: A first linear algebra course, proofs
- Level: Undergrad
Table of Contents:
Code:
[LIST]
[*] Linear Equations
[LIST]
[*] Fields
[*] Systems of Linear Equations
[*] Matrices and Elementary Row Operations
[*] Row-Reduced Echelon Matrices
[*] Matrix Multiplication
[*] Invertible Matrices
[/LIST]
[*] Vector Spaces
[LIST]
[*] Vector Spaces
[*] Subspaces
[*] Bases and Dimension
[*] Coordinates
[*] Summary of Row-Equivalence
[*] Computations Concerning Subspaces
[/LIST]
[*] Linear Transformations
[LIST]
[*] Linear Transformations
[*] The Algebra of Linear Transformations
[*] Isomorphism
[*] Representation of Transformations by Matrices
[*] Linear Functionals
[*] The Double Dual
[*] The Transpose of a Linear Transformation
[/LIST]
[*] Polynomials
[LIST]
[*] Algebras
[*] The Algebra of Polynomials
[*] Lagrange Interpolation
[*] Polynomial Ideals
[*] The Prime Factorization of a Polynomial
[/LIST]
[*] Determinants
[LIST]
[*] Commutative Rings
[*] Determinant Functions
[*] Permutation and the Uniqueness of Determinants
[*] Additional Properties of Determinants
[*] Modules
[*] Multilinear Functions
[*] The Grassman Ring
[/LIST]
[*] Elementary Canonical Forms
[LIST]
[*] Introduction
[*] Characteristic Values
[*] Annihilating Polynomials
[*] Invariant Subspaces
[*] Simultaneous Triangulation; Simultaneaous Diagonalization
[*] Direct-Sum Decompositions
[*] Invariant Direct sums
[*] The Primary Decomposition Theorem
[/LIST]
[*] The Rational and Jordan Forms
[LIST]
[*] Cyclic Subspaces and Annihilators
[*] Cyclic Decompositions and the Rational Form
[*] The Jordan Form
[*] Computation of Invariant Factors
[*] Summary; Semi-Simple Operators
[/LIST]
[*] Inner Product Spaces
[LIST]
[*] Inner Products
[*] Inner Product Spaces
[*] Linear Functionals and Adjoints
[*] Unitary Operators
[*] Normal Operators
[/LIST]
[*] Operators on Inner Product Spaces
[LIST]
[*] Introduction
[*] Forms on Inner Product Spaces
[*] Positive Forms
[*] More on Forms
[*] Spectral Theory
[*] Further Properties of Normal Operators
[/LIST]
[*] Bilinear Forms
[LIST]
[*] Bilinear Forms
[*] Symmetric Bilinear Forms
[*] Skew-Symmetric Bilinear Forms
[*] Groups Preserving Bilinear Forms
[/LIST]
[*] Appendix
[LIST]
[*] Sets
[*] Functions
[*] Equivalence Relations
[*] Quotient Spaces
[*] Equivalence Relations in Linear Algebra
[*] The Axiom of Choice
[/LIST]
[*] Bibliography
[*] Index
[/LIST]
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