Elementary Linear Algebra: applications version / Howard Anton ,Chris Rorres.

By:

Anton, Howard

Contributor(s):

Rorres, Chris

Material type: Text

TextPublication details: New York ; John Wiley & Sons Inc: 2005.Edition: 9th edDescription: 832 p. : ill ; 27 cmISBN:

9780471449027

Subject(s):

Algebras, -- Linear

DDC classification:

512.5

Contents:

Chapter 1 Systems of Linear Equations and Matrices 1 -- 1.1 Introduction to Systems of Linear Equations 2 -- 1.2 Gaussian Elimination 8 -- 1.3 Matrices and Matrix Operations 23 -- 1.4 Inverses; Rules of Matrix Arithmetic 39 -- 1.5 Elementary Matrices and a Method for Finding A[superscript -1] 51 -- 1.6 Further Results on Systems of Equations and Invertibility 60 -- 1.7 Diagonal, Triangular, and Symmetric Matrices 68 -- Chapter 2 Determinants 83 -- 2.1 Determinants by Cofactor Expansion 84 -- 2.2 Evaluating Determinants by Row Reduction 96 -- 2.3 Properties of the Determinant Function 103 -- 2.4 A Combinatorial Approach to Determinants 111 -- Chapter 3 Vectors in 2-Space and 3-Space 123 -- 3.1 Introduction to Vectors (Geometric) 124 -- 3.2 Norm of a Vector; Vector Arithmetic 131 -- 3.3 Dot Product; Projections 136 -- 3.4 Cross Product 144 -- 3.5 Lines and Planes in 3-Space 156 -- Chapter 4 Euclidean Vector Spaces 167 -- 4.1 Euclidean n-Space 168 -- 4.2 Linear Transformations from R[superscript n] to R[superscript m] 181 -- 4.3 Properties of Linear Transformations from R[superscript n] to R[superscript m] 197 -- 4.4 Linear Transformations and Polynomials 210 -- Chapter 5 General Vector Spaces 221 -- 5.1 Real Vector Spaces 222 -- 5.2 Subspaces 229 -- 5.3 Linear Independence 240 -- 5.4 Basis and Dimension 250 -- 5.5 Row Space, Column Space, and Nullspace 266 -- 5.6 Rank and Nullity 279 -- Chapter 6 Inner Product Spaces 295 -- 6.1 Inner Products 296 -- 6.2 Angle and Orthogonality in Inner Product Spaces 307 -- 6.3 Orthonormal Bases; Gram-Schmidt Prodcess; QR-Decomposition 318 -- 6.4 Best Approximation; Least Squares 332 -- 6.5 Change of Basis 341 -- 6.6 Orthogonal Matrices 347 -- Chapter 7 Eigenvalues, Eigenvectors 359 -- 7.1 Eigenvalues and Eigenvectors 360 -- 7.2 Diagonalization 369 -- 7.3 Orthogonal Diagonalization 380 -- Chapter 8 Linear Transformations 389 -- 8.1 General Linear Transformations 390 -- 8.2 Kernel and Range 400 -- 8.3 Inverse Linear Transformations 407 -- 8.4 Matrices of General Linear Transformations 416 -- 8.5 Similarity 430 -- 8.6 Isomorphism 442 -- 9.1 Application to Differential Equations 452 -- 9.2 Geometry of Linear Operators on R[superscript 2] 458 -- 9.3 Least Squares Fitting to Data 468 -- 9.4 Approximation Problems; Fourier Series 474 -- 9.5 Quadratic Forms 479 -- 9.6 Diagonalizing Quadratic Forms; Conic Sections 487 -- 9.7 Quadric Surfaces 497 -- 9.8 Comparison of Procedures for Solving Linear Systems 502 -- 9.9 LU-Decompositions 511 -- Chapter 10 Complex Vector Spaces 521 -- 10.1 Complex Numbers 522 -- 10.2 Division of Complex Numbers 528 -- 10.3 Polar Form of a Complex Number 533 -- 10.4 Complex Vector Spaces 540 -- 10.5 Complex Inner Product Spaces 547 -- 10.6 Unitary Normal, and Hermitian Matrices 554 -- Chapter 11 Applications of Linear Algebra 567 -- 11.1 Constructing Curves and Surfaces through Specified Points 568 -- 11.2 Electrical Networks 574 -- 11.3 Geometric Linear Programming 578 -- 11.4 The Earliest Applications of Linear Algebra 590 -- 11.5 Cubic Spline Interpolation 597 -- 11.6 Markov Chains 608 -- 11.7 Graph Theory 619 -- 11.8 Games of Strategy 629 -- 11.9 Leontief Economic Models 639 -- 11.10 Forest Management 648 -- 11.11 Computer Graphics 657 -- 11.12 Equilibrium Temperature Distributions 665 -- 11.13 Computed Tomography 676 -- 11.14 Fractals 688 -- 11.15 Chaos 705 -- 11.16 Cryptography 719 -- 11.17 Genetics 732 -- 11.18 Age-Specific Population Growth 743 -- 11.19 Harvesting of Animal Populations 753 -- 11.20 A Least Squares Model for Human Hearing 762 -- 11.21 Warps and Morphs 768.

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Holdings
Item type	Current library	Call number	Status	Date due	Barcode
Books	Main library	512.5/AN.E (Browse shelf(Opens below))	Available		016533

Chapter 1 Systems of Linear Equations and Matrices 1 --
1.1 Introduction to Systems of Linear Equations 2 --
1.2 Gaussian Elimination 8 --
1.3 Matrices and Matrix Operations 23 --
1.4 Inverses; Rules of Matrix Arithmetic 39 --
1.5 Elementary Matrices and a Method for Finding A[superscript -1] 51 --
1.6 Further Results on Systems of Equations and Invertibility 60 --
1.7 Diagonal, Triangular, and Symmetric Matrices 68 --
Chapter 2 Determinants 83 --
2.1 Determinants by Cofactor Expansion 84 --
2.2 Evaluating Determinants by Row Reduction 96 --
2.3 Properties of the Determinant Function 103 --
2.4 A Combinatorial Approach to Determinants 111 --
Chapter 3 Vectors in 2-Space and 3-Space 123 --
3.1 Introduction to Vectors (Geometric) 124 --
3.2 Norm of a Vector; Vector Arithmetic 131 --
3.3 Dot Product; Projections 136 --
3.4 Cross Product 144 --
3.5 Lines and Planes in 3-Space 156 --
Chapter 4 Euclidean Vector Spaces 167 --
4.1 Euclidean n-Space 168 --
4.2 Linear Transformations from R[superscript n] to R[superscript m] 181 --
4.3 Properties of Linear Transformations from R[superscript n] to R[superscript m] 197 --
4.4 Linear Transformations and Polynomials 210 --
Chapter 5 General Vector Spaces 221 --
5.1 Real Vector Spaces 222 --
5.2 Subspaces 229 --
5.3 Linear Independence 240 --
5.4 Basis and Dimension 250 --
5.5 Row Space, Column Space, and Nullspace 266 --
5.6 Rank and Nullity 279 --
Chapter 6 Inner Product Spaces 295 --
6.1 Inner Products 296 --
6.2 Angle and Orthogonality in Inner Product Spaces 307 --
6.3 Orthonormal Bases; Gram-Schmidt Prodcess; QR-Decomposition 318 --
6.4 Best Approximation; Least Squares 332 --
6.5 Change of Basis 341 --
6.6 Orthogonal Matrices 347 --
Chapter 7 Eigenvalues, Eigenvectors 359 --
7.1 Eigenvalues and Eigenvectors 360 --
7.2 Diagonalization 369 --
7.3 Orthogonal Diagonalization 380 --
Chapter 8 Linear Transformations 389 --
8.1 General Linear Transformations 390 --
8.2 Kernel and Range 400 --
8.3 Inverse Linear Transformations 407 --
8.4 Matrices of General Linear Transformations 416 --
8.5 Similarity 430 --
8.6 Isomorphism 442 --
9.1 Application to Differential Equations 452 --
9.2 Geometry of Linear Operators on R[superscript 2] 458 --
9.3 Least Squares Fitting to Data 468 --
9.4 Approximation Problems; Fourier Series 474 --
9.5 Quadratic Forms 479 --
9.6 Diagonalizing Quadratic Forms; Conic Sections 487 --
9.7 Quadric Surfaces 497 --
9.8 Comparison of Procedures for Solving Linear Systems 502 --
9.9 LU-Decompositions 511 --
Chapter 10 Complex Vector Spaces 521 --
10.1 Complex Numbers 522 --
10.2 Division of Complex Numbers 528 --
10.3 Polar Form of a Complex Number 533 --
10.4 Complex Vector Spaces 540 --
10.5 Complex Inner Product Spaces 547 --
10.6 Unitary Normal, and Hermitian Matrices 554 --
Chapter 11 Applications of Linear Algebra 567 --
11.1 Constructing Curves and Surfaces through Specified Points 568 --
11.2 Electrical Networks 574 --
11.3 Geometric Linear Programming 578 --
11.4 The Earliest Applications of Linear Algebra 590 --
11.5 Cubic Spline Interpolation 597 --
11.6 Markov Chains 608 --
11.7 Graph Theory 619 --
11.8 Games of Strategy 629 --
11.9 Leontief Economic Models 639 --
11.10 Forest Management 648 --
11.11 Computer Graphics 657 --
11.12 Equilibrium Temperature Distributions 665 --
11.13 Computed Tomography 676 --
11.14 Fractals 688 --
11.15 Chaos 705 --
11.16 Cryptography 719 --
11.17 Genetics 732 --
11.18 Age-Specific Population Growth 743 --
11.19 Harvesting of Animal Populations 753 --
11.20 A Least Squares Model for Human Hearing 762 --
11.21 Warps and Morphs 768.

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