Chapter1.LinearEquations
1.1.Fields
1.2.SystemsofLinearEquations
1.3.MatricesandElementaryRowOperations
1.4.Row-ReducedEchelonMatrices
1.5.MatrixMultiplication
1.6.InvertibleMatrices
Chapter2.VectorSpaces
2.1.VectorSpaces
2.2.Subspaces
2.3.BasesandDimension
2.4.Coordinates
2.5.SummaryofRow-Equivalence
2.6.ComputationsConcerningSubspaces
Chapter3.LinearTransformations
3.1.LinearTransformations
3.2.TheAlgebraofLinearTransformations
3.3.Isomorphism
3.4.RepresentationofTransformationsbyMatrices
3.5.LinearFunctionals
3.6.TheDoubleDual
3.7.TheTransposeofaLinearTransformation
Chapter4.Polynomials
4.1.Algebras
4.2.TheAlgebraofPolynomials
4.3.LagrangeInterpolation
4.4.PolynomialIdeals
4.5.ThePrimeFactorizationofaPolynomial
Chapter5.Determinants
5.1.CommutativeRings
5.2.DeterminantFunctions
5.3.PermutationsandtheUniquenessofDeterminants
5.4.AdditionalPropertiesofDeterminants
5.5.Modules
5.6.MultilinearFunctions
5.7.TheGrassmanRing
Chapter6.ElementaryCanonicalForms
6.1.Introduction
6.2.CharacteristicValues
6.3..AnnihilatingPolynomials
6.4.InvariantSubspaces
6.5.simultaneousTriangulation;SimultaneousDiagonalization
6.6.Direct-SumDecompositions
6.7.InvarlantDirectSums
6.8.ThePrimaryDecompositionTheorem
Chapter7.TheRationalandJordanForms
7.1.CyclicSubspacesandAnnihilators
7.2.CyclicDecompositionsandtheRationalForm
7.3.TheJordanForm
7.4.ComputationofInvarlantFactors
7.5.Summary;Semi-SimpleOperators
Chapter8.InnerProductSpaces
8.1.InnerProducts
8.2.InnerProductSpaces
8.3.LinearFunctional]andAdjoints
8.4.UnitaryOperators
8.5.NormalOperators
Chapter9.OperatorsonInnerProductSpaces
9.1.Introduction
9.2.FormsonInnerProductSpaces
9.3.PositiveForms
9.4.MoreonForms
9.5.SpectralTheory
9.6.FurtherPropertiesofNormalOperators
Chapter10.BilinearForms
10.1.BilinearForms
10.2.SymmetricBilinearForms
10.3.Skew-SymmetricBilinearForms
10.4GroupsPreservingBilinearForms
Appendix
A.1.Sets
A.2.Functions
A.3.EquivalenceRelations
A.4.QuotientSpaces
A.5.EquivalenceRelationsinLinearAlgebra
A.6.TheAxiomofChoice
Bibliography
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