Preface to the Second EditionPreface to the First EditionAcknowledgmentsList of FiguresSymbol DescriptionVector SpacesFieldsThe Space â £nVector Spaces over an Arbitrary FieldSubspaces of Vector SpacesSpan and IndependenceBases and Finite-Dimensional Vector SpacesBases and Infinite-Dimensional Vector SpacesCoordinate VectorsLinear TransformationsIntroduction to Linear TransformationsThe Range and Kernel of a Linear TransformationThe Correspondence and Isomorphism TheoremsMatrix of a Linear TransformationThe Algebra of L(V, W) and Mmn(â £) Invertible Transformations and MatricesPolynomialsThe Algebra of PolynomialsRoots of PolynomialsTheory of a Single Linear OperatorInvariant Subspaces of an OperatorCyclic OperatorsMaximal VectorsIndecomposable Linear OperatorsInvariant Factors and Elementary DivisorsCanonical FormsOperators on Real and Complex Vector SpacesNormed and Inner Product SpacesInner ProductsGeometry in Inner Product SpacesOrthonormal Sets and the Gram-Schmidt ProcessOrthogonal Complements and ProjectionsDual SpacesAdjointsNormed Vector SpacesLinear Operators on Inner Product SpacesSelf-Adjoint and Normal OperatorsSpectral TheoremsNormal Operators on Real Inner Product SpacesUnitary and Orthogonal OperatorsThe Polar Decomposition and Singular Value DecompositionTrace and Determinant of a Linear OperatorTrace of a Linear OperatorDeterminant of a Linear Operator and MatrixUniqueness of the Determinant of a Linear OperatorBilinear FormsBasic Properties of Bilinear MapsSymplectic SpacesQuadratic Forms and Orthogonal SpaceOrthogonal Space, Characteristic TwoReal Quadratic FormsSesquilinear Forms and Unitary GeometryBasic Properties of Sesquilinear FormsUnitary SpaceTensor ProductsIntroduction to Tensor ProductsProperties of Tensor ProductsThe Tensor AlgebraThe Symmetric AlgebraThe Exterior AlgebraClifford Algebras, char â £ â 2Linear Groups and Groups of IsometriesLinear GroupsSymplectic GroupsOrthogonal Groups, char â £ â 2 Unitary GroupsAdditional Topics in Linear AlgebraMatrix NormsThe Moore-Penrose Inverse of a MatrixNonnegative MatricesThe Location of EigenvaluesFunctions of MatricesApplications of Linear AlgebraLeast SquaresError Correcting CodesRanking Webpages for Search EnginesAppendicesConcepts from Topology and AnalysisConcepts from Group TheoryAnswers to Selected ExercisesHints to Selected ProblemsBibliographyIndex