Elementary Linear Algebra, Application Version, International Adaptation, Revised Edition - Anton Kaul

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Résumé :

1 Systems of Linear Equations and Matrices 1

1.1 Introduction to Systems of Linear Equations 2

1.2 Gaussian Elimination 11

1.3 Matrices and Matrix Operations 25

1.4 Inverses...

Biographie:
Cramer's Rule 134

3 Euclidean Vector Spaces 149

3.1 Vectors in 2-Space, 3-Space, and n-Space 149

3.2 Norm, Dot Product, and Distance in R n 161

3.3 Orthogonality 175

3.4 The Geometry of Linear Systems 186

3.5 Cross Product 193

4 General Vector Spaces 205

4.1 Real Vector Spaces 205

4.2 Subspaces 214

4.3 Spanning Sets 223

4.4 Linear Independence 231

4.5 Coordinates and Basis 241

4.6 Dimension 251

4.7 Change of Basis 259

4.8 Row Space, Column Space, and Null Space 266

4.9 Rank, Nullity, and the Fundamental Matrix Spaces 279

5 Eigenvalues and Eigenvectors 295

5.1 Eigenvalues and Eigenvectors 295

5.2 Diagonalization 305

5.3 Complex Vector Spaces 315

5.4 Differential Equations 327

5.5 Dynamical Systems and Markov Chains 333

6 Inner Product Spaces 347

6.1 Inner Products 347

6.2 Angle and Orthogonality in Inner Product Spaces 358

6.3 Gram-Schmidt Process...

Sommaire:
Algebraic Properties of Matrices 40

1.5 Elementary Matrices and a Method for Finding A - 1 53

1.6 More on Linear Systems and Invertible Matrices 62

1.7 Diagonal, Triangular, and Symmetric Matrices 69

1.8 Introduction to Linear Transformations 76

1.9 Compositions of Matrix Transformations 90

1.10 Applications of Linear Systems 98

Network Analysis 98

Electrical Circuits 100

Balancing Chemical Equations 103

Polynomial Interpolation 105

1.11 Leontief Input-Output Models 110

2 Determinants 119

2.1 Determinants by Cofactor Expansion 119

2.2 Evaluating Determinants by Row Reduction 127

2.3 Properties of Determinants...