{"product_id":"elementary-linear-algebra-applications-version-australia-and-new-zealand-edition","title":"Elementary Linear Algebra, Applications Version, Australia and New Zealand Edition","description":"\u003cp\u003e\u003cb\u003e1 \u003c\/b\u003e\u003cb\u003eSystems of Linear Equations and Matrices 1\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e1.1 Introduction to Systems of Linear Equations 2\u003c\/p\u003e \u003cp\u003e1.2 Gaussian Elimination 11\u003c\/p\u003e \u003cp\u003e1.3 Matrices and Matrix Operations 25\u003c\/p\u003e \u003cp\u003e1.4 Inverses; Algebraic Properties of Matrices 40\u003c\/p\u003e \u003cp\u003e1.5 Elementary Matrices and a Method for Finding \u003ci\u003eA\u003c\/i\u003e\u003csup\u003e−1\u003c\/sup\u003e 53\u003c\/p\u003e \u003cp\u003e1.6 More on Linear Systems and Invertible Matrices 62\u003c\/p\u003e \u003cp\u003e1.7 Diagonal, Triangular, and Symmetric Matrices 69\u003c\/p\u003e \u003cp\u003e1.8 Introduction to Linear Transformations 76\u003c\/p\u003e \u003cp\u003e1.9 Compositions of Matrix Transformations 90\u003c\/p\u003e \u003cp\u003e1.10 Applications of Linear Systems 98\u003c\/p\u003e \u003cp\u003e• Network Analysis 98\u003c\/p\u003e \u003cp\u003e• Electrical Circuits 100\u003c\/p\u003e \u003cp\u003e• Balancing Chemical Equations 103\u003c\/p\u003e \u003cp\u003e• Polynomial Interpolation 105\u003c\/p\u003e \u003cp\u003e1.11 Leontief Input-Output Models 110\u003c\/p\u003e \u003cp\u003e\u003cb\u003e2 \u003c\/b\u003e\u003cb\u003eDeterminants 118\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e2.1 Determinants by Cofactor Expansion 118\u003c\/p\u003e \u003cp\u003e2.2 Evaluating Determinants by Row Reduction 126\u003c\/p\u003e \u003cp\u003e2.3 Properties of Determinants; Cramer’s Rule 133\u003c\/p\u003e \u003cp\u003e\u003cb\u003e3 \u003c\/b\u003e\u003cb\u003eEuclidean Vector Spaces 146\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e3.1 Vectors in 2-Space, 3-Space, and \u003ci\u003en\u003c\/i\u003e-Space 146\u003c\/p\u003e \u003cp\u003e3.2 Norm, Dot Product, and Distance in \u003ci\u003eR\u003csup\u003en \u003c\/sup\u003e\u003c\/i\u003e158\u003c\/p\u003e \u003cp\u003e3.3 Orthogonality 172\u003c\/p\u003e \u003cp\u003e3.4 The Geometry of Linear Systems 183\u003c\/p\u003e \u003cp\u003e3.5 Cross Product 190\u003c\/p\u003e \u003cp\u003e\u003cb\u003e4 \u003c\/b\u003e\u003cb\u003eGeneral Vector Spaces 202\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e4.1 Real Vector Spaces 202\u003c\/p\u003e \u003cp\u003e4.2 Subspaces 211\u003c\/p\u003e \u003cp\u003e4.3 Spanning Sets 220\u003c\/p\u003e \u003cp\u003e4.4 Linear Independence 228\u003c\/p\u003e \u003cp\u003e4.5 Coordinates and Basis 238\u003c\/p\u003e \u003cp\u003e4.6 Dimension 248\u003c\/p\u003e \u003cp\u003e4.7 Change of Basis 256\u003c\/p\u003e \u003cp\u003e4.8 Row Space, Column Space, and Null Space 263\u003c\/p\u003e \u003cp\u003e4.9 Rank, Nullity, and the Fundamental Matrix Spaces 276\u003c\/p\u003e \u003cp\u003e\u003cb\u003e5 \u003c\/b\u003e\u003cb\u003eEigenvalues and Eigenvectors 291\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e5.1 Eigenvalues and Eigenvectors 291\u003c\/p\u003e \u003cp\u003e5.2 Diagonalization 301\u003c\/p\u003e \u003cp\u003e5.3 Complex Vector Spaces 311\u003c\/p\u003e \u003cp\u003e5.4 Differential Equations 323\u003c\/p\u003e \u003cp\u003e5.5 Dynamical Systems and Markov Chains 329\u003c\/p\u003e \u003cp\u003e\u003cb\u003e6 \u003c\/b\u003e\u003cb\u003eInner Product Spaces 341\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e6.1 Inner Products 341\u003c\/p\u003e \u003cp\u003e6.2 Angle and Orthogonality in Inner Product Spaces 352\u003c\/p\u003e \u003cp\u003e6.3 Gram–Schmidt Process; \u003ci\u003eQR\u003c\/i\u003e-Decomposition 361\u003c\/p\u003e \u003cp\u003e6.4 Best Approximation; Least Squares 376\u003c\/p\u003e \u003cp\u003e6.5 Mathematical Modeling Using Least Squares 385\u003c\/p\u003e \u003cp\u003e6.6 Function Approximation; Fourier Series 392\u003c\/p\u003e \u003cp\u003e\u003cb\u003e7 \u003c\/b\u003e\u003cb\u003eDiagonalization and Quadratic Forms 399\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e7.1 Orthogonal Matrices 399\u003c\/p\u003e \u003cp\u003e7.2 Orthogonal Diagonalization 408\u003c\/p\u003e \u003cp\u003e7.3 Quadratic Forms 416\u003c\/p\u003e \u003cp\u003e7.4 Optimization Using Quadratic Forms 429\u003c\/p\u003e \u003cp\u003e7.5 Hermitian, Unitary, and Normal Matrices 436\u003c\/p\u003e \u003cp\u003e\u003cb\u003e8 \u003c\/b\u003e\u003cb\u003eGeneral Linear Transformations 446\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e8.1 General Linear Transformations 446\u003c\/p\u003e \u003cp\u003e8.2 Compositions and Inverse Transformations 459\u003c\/p\u003e \u003cp\u003e8.3 Isomorphism 471\u003c\/p\u003e \u003cp\u003e8.4 Matrices for General Linear Transformations 477\u003c\/p\u003e \u003cp\u003e8.5 Similarity 487\u003c\/p\u003e \u003cp\u003e8.6 Geometry of Matrix Operators 493\u003c\/p\u003e \u003cp\u003e\u003cb\u003e9 \u003c\/b\u003e\u003cb\u003eNumerical Methods 509\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e9.1 \u003ci\u003eLU\u003c\/i\u003e-Decompositions 509\u003c\/p\u003e \u003cp\u003e9.2 The Power Method 519\u003c\/p\u003e \u003cp\u003e9.3 Comparison of Procedures for Solving Linear Systems 528\u003c\/p\u003e \u003cp\u003e9.4 Singular Value Decomposition 532\u003c\/p\u003e \u003cp\u003e9.5 Data Compression Using Singular Value Decomposition 540\u003c\/p\u003e \u003cp\u003e\u003cb\u003e10 \u003c\/b\u003e\u003cb\u003eApplications of Linear Algebra 545\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e10.1 Constructing Curves and Surfaces Through Specified Points 546\u003c\/p\u003e \u003cp\u003e10.2 The Earliest Applications of Linear Algebra 551\u003c\/p\u003e \u003cp\u003e10.3 Cubic Spline Interpolation 558\u003c\/p\u003e \u003cp\u003e10.4 Markov Chains 568\u003c\/p\u003e \u003cp\u003e10.5 Graph Theory 577\u003c\/p\u003e \u003cp\u003e10.6 Games of Strategy 587\u003c\/p\u003e \u003cp\u003e10.7 Forest Management 595\u003c\/p\u003e \u003cp\u003e10.8 Computer Graphics 602\u003c\/p\u003e \u003cp\u003e10.9 Equilibrium Temperature Distributions 610\u003c\/p\u003e \u003cp\u003e10.10 Computed Tomography 619\u003c\/p\u003e \u003cp\u003e10.11 Fractals 629\u003c\/p\u003e \u003cp\u003e10.12 Chaos 645\u003c\/p\u003e \u003cp\u003e10.13 Cryptography 658\u003c\/p\u003e \u003cp\u003e10.14 Genetics 669\u003c\/p\u003e \u003cp\u003e10.15 Age-Specific Population Growth 678\u003c\/p\u003e \u003cp\u003e10.16 Harvesting of Animal Populations 687\u003c\/p\u003e \u003cp\u003e10.17 A Least Squares Model for Human Hearing 695\u003c\/p\u003e \u003cp\u003e10.18 Warps and Morphs 701\u003c\/p\u003e \u003cp\u003e10.19 Internet Search Engines 710\u003c\/p\u003e \u003cp\u003e10.20 Facial Recognition 716\u003c\/p\u003e \u003cp\u003e\u003cb\u003eSupplemental Online Topics\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e• Linear Programming - A Geometric Approach\u003c\/p\u003e \u003cp\u003e• Linear Programming - Basic Concepts\u003c\/p\u003e \u003cp\u003e• Linear Programming - The Simplex Method\u003c\/p\u003e \u003cp\u003e• Vectors in Plane Geometry\u003c\/p\u003e \u003cp\u003e• Equilibrium of Rigid Bodies\u003c\/p\u003e \u003cp\u003e• The Assignment Problem\u003c\/p\u003e \u003cp\u003e• The Determinant Function\u003c\/p\u003e \u003cp\u003e• Leontief Economic Models\u003c\/p\u003e \u003cp\u003eAppendix A Working with Proofs A1\u003c\/p\u003e \u003cp\u003eAppendix B Complex Numbers A5\u003c\/p\u003e \u003cp\u003eAnswers to Exercises A13\u003c\/p\u003e \u003cp\u003eIndex I1\u003c\/p\u003e","brand":"Anton Kaul","offers":[{"title":"Default Title","offer_id":42818413625405,"sku":"9781119666066","price":148.45,"currency_code":"AUD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0597\/7689\/2989\/files\/9781119666066_9c07f436-623c-43af-a6fe-c1ef385caa84.jpg?v=1766919844","url":"https:\/\/www.palmleaf.com.au\/products\/elementary-linear-algebra-applications-version-australia-and-new-zealand-edition","provider":"Palmleaf","version":"1.0","type":"link"}