04582nam 2200625 450 991046083400332120200520144314.01-118-90962-3(CKB)3710000000493640(EBL)4435623(SSID)ssj0001570656(PQKBManifestationID)16221773(PQKBTitleCode)TC0001570656(PQKBWorkID)14835953(PQKB)11001324(MiAaPQ)EBC4435623(DLC) 2015017737(JP-MeL)3000065408(PPN)195533615(Au-PeEL)EBL4435623(CaPaEBR)ebr11169628(CaONFJC)MIL902561(OCoLC)908311273(EXLCZ)99371000000049364020160331h20162016 uy 0engur|n|---|||||txtccrLinear algebra ideas and applications /Richard PenneyFourth edition.Hoboken, New Jersey :Wiley,2016.©20161 online resource (513 p.)Includes index.1-118-90958-5 Linear Algebra; Contents; Preface; Features of the Text; Acknowledgments; About the Companion Website; Chapter 1 Systems of Linear Equations; 1.1 The Vector Space of Matrices; The Space Rn; Linear Combinations and Linear Dependence; What Is a Vector Space?; Why Prove Anything?; Exercises; 1.1.1 Computer Projects; Exercises; 1.1.2 Applications to Graph Theory I; Self-Study Questions; Exercises; 1.2 Systems; Rank: The Maximum Number of Linearly Independent Equations; Exercises; 1.2.1 Computer Projects; Exercises; 1.2.2 Applications to Circuit Theory; Self-Study QuestionsExercises1.3 Gaussian Elimination; Spanning in Polynomial Spaces; Computational Issues: Pivoting; Exercises; Computational Issues: Counting Flops; 1.3.1 Computer Projects; Exercises; Applications to Traffic Flow; Self-Study Questions; Exercises; 1.4 Column Space and Nullspace; Subspaces; Exercises; Computer Projects; Chapter Summary; Chapter 2 Linear Independence and Dimension; 2.1 The Test for Linear Independence; Bases for the Column Space; Testing Functions for Independence; Exercises; 2.1.1 Computer Projects ; Exercises; 2.2 Dimension; Exercises; 2.2.1 Computer ProjectsExercises2.2.2 Applications to Differential Equations; Exercises; 2.3 Row Space and the rank-nullity theorem; Bases for the Row Space; Summary; Computational Issues: Computing Rank; Exercises; 2.3.1 Computer Projects; Exercises; Chapter Summary; Chapter 3 Linear Transformations; 3.1 The Linearity Properties; Exercises; 3.1.1 Computer Projects; Exercises; 3.2 Matrix Multiplication (Composition); Partitioned Matrices; Computational Issues: Parallel Computing; Exercises; 3.2.1 Computer Projects; Exercises; 3.2.2 Applications to Graph Theory II; Self-Study Questions; Exercises3.3 Inverses Computational Issues: Reduction versus Inverses; Exercises; 3.3.1 Computer Projects; Exercises; 3.3.2 Applications to Economics; Self-Study Questions; Exercises; 3.4 The LU Factorization; Exercises; 3.4.1 Computer Projects; Exercises; 3.5 The Matrix of a Linear Transformation; Coordinates; Application to Differential Equations; Isomorphism; Invertible Linear Transformations; Exercises; Computer Projects; Exercises; Chapter Summary; Chapter 4 Determinants; 4.1 Definition of the Determinant; 4.1.1 The Rest of the Proofs; Exercises; 4.1.2 Computer Projects4.2 Reduction and Determinants Uniqueness of the Determinant; Exercises; 4.2.1 Volume; Exercises; A Formula for Inverses; Exercises; Chapter Summary; Chapter 5 Eigenvectors and Eigenvalues; 5.1 Eigenvectors; Exercises; 5.1.1 Computer Projects; Exercises; 5.1.2 Application to Markov Processes; Exercises; 5.2 Diagonalization; Powers of Matrices; Exercises; 5.2.1 Computer Projects; Exercises; 5.2.2 Application to Systems of Differential Equations; Exercises; 5.3 Complex Eigenvectors; Complex Vector Spaces; Exercises; 5.3.1 Computer Projects; 5.3 Exercises; Chapter SummaryChapter 6 OrthogonalityAlgebras, LinearTextbooksElectronic books.Algebras, Linear512/.5Penney Richard C.872347MiAaPQMiAaPQMiAaPQBOOK9910460834003321Linear algebra1947612UNINA