Linear algebra and its applications / David C. Lay.

Includes index.

engineering bookfair2015

<P><B>1. Linear Equations in Linear Algebra</B></P><P>Introductory Example: Linear Models in Economics and Engineering</P><P>1.1 Systems of Linear Equations</P><P>1.2 Row Reduction and Echelon Forms</P><P>1.3 Vector Equations</P><P>1.4 The Matrix Equation <I>Ax</I> = <I>b</I></P><P>1.5 Solution Sets of Linear Systems</P><P>1.6 Applications of Linear Systems</P><P>1.7 Linear Independence</P><P>1.8 Introduction to Linear Transformations</P><P>1.9 The Matrix of a Linear Transformation</P><P>1.10 Linear Models in Business, Science, and Engineering</P><P>Supplementary Exercises</P><P> </P><P><B>2. Matrix Algebra</B></P><P>Introductory Example: Computer Models in Aircraft Design</P><P>2.1 Matrix Operations</P><P>2.2 The Inverse of a Matrix</P><P>2.3 Characterizations of Invertible Matrices</P><P>2.4 Partitioned Matrices</P><P>2.5 Matrix Factorizations</P><P>2.6 The Leontief Inputâ Output Model</P><P>2.7 Applications to Computer Graphics</P><P>2.8 Subspaces of <I>Rn</I></P><P>2.9 Dimension and Rank</P><P>Supplementary Exercises</P><P> </P><P><B>3. Determinants</B></P><P>Introductory Example: Random Paths and Distortion</P><P>3.1 Introduction to Determinants</P><P>3.2 Properties of Determinants</P><P>3.3 Cramerâ s Rule, Volume, and Linear Transformations</P><P>Supplementary Exercises</P><P> </P><P><B>4. Vector Spaces</B></P><P>Introductory Example: Space Flight and Control Systems</P><P>4.1 Vector Spaces and Subspaces</P><P>4.2 Null Spaces, Column Spaces, and Linear Transformations</P><P>4.3 Linearly Independent Sets; Bases</P><P>4.4 Coordinate Systems</P><P>4.5 The Dimension of a Vector Space</P><P>4.6 Rank</P><P>4.7 Change of Basis</P><P>4.8 Applications to Difference Equations</P><P>4.9 Applications to Markov Chains</P><P>Supplementary Exercises</P><P> </P><P><B>5. Eigenvalues and Eigenvectors</B></P><P>Introductory Example: Dynamical Systems and Spotted Owls</P><P>5.1 Eigenvectors and Eigenvalues</P><P>5.2 The Characteristic Equation</P><P>5.3 Diagonalization</P><P>5.4 Eigenvectors and Linear Transformations</P><P>5.5 Complex Eigenvalues</P><P>5.6 Discrete Dynamical Systems</P><P>5.7 Applications to Differential Equations</P><P>5.8 Iterative Estimates for Eigenvalues</P><P>Supplementary Exercises</P><P> </P><P><B>6. Orthogonality and Least Squares</B></P><P>Introductory Example: Readjusting the North American Datum</P><P>6.1 Inner Product, Length, and Orthogonality</P><P>6.2 Orthogonal Sets</P><P>6.3 Orthogonal Projections</P><P>6.4 The Gramâ Schmidt Process</P><P>6.5 Least-Squares Problems</P><P>6.6 Applications to Linear Models</P><P>6.7 Inner Product Spaces</P><P>6.8 Applications of Inner Product Spaces</P><P>Supplementary Exercises</P><P> </P><P><B>7. Symmetric Matrices and Quadratic Forms</B></P><P>Introductory Example: Multichannel Image Processing</P><P>7.1 Diagonalization of Symmetric Matrices</P><P>7.2 Quadratic Forms</P><P>7.3 Constrained Optimization</P><P>7.4 The Singular Value Decomposition</P><P>7.5 Applications to Image Processing and Statistics</P><P>Supplementary Exercises</P><P> </P><P><B>8. The Geometry of Vector Spaces</B></P><P>Introductory Example: The Platonic Solids</P><P>8.1 Affine Combinations</P><P>8.2 Affine Independence</P><P>8.3 Convex Combinations</P><P>8.4 Hyperplanes</P><P>8.5 Polytopes</P><P>8.6 Curves and Surfaces</P><P> </P><P><B>9. Optimization (Online Only)</B></P><P>Introductory Example: The Berlin Airlift</P><P>9.1 Matrix Games</P><P>9.2 Linear Programmingâ Geometric Method</P><P>9.3 Linear Programmingâ Simplex Method</P><P>9.4 Duality</P><P> </P><P><B>10. Finite-State Markov Chains (Online Only)</B></P><P>Introductory Example: Google and Markov Chains</P><P>10.1 Introduction and Examples</P><P>10.2 The Steady-State Vector and Google's PageRank</P><P>10.3 Finite-State Markov Chains</P><P>10.4 Classification of States and Periodicity</P><P>10.5 The Fundamental Matrix</P><P>10.6 Markov Chains and Baseball Statistics</P><P> </P><P><B>Appendices</B></P><P>A. Uniqueness of the Reduced Echelon Form</P><P>B. Complex Numbers</P>