Includes index.

Chapter 1. Systems of Linear Equations and Matrices. 1.1 Introduction to Systems of Linear Equations. 1.2 Gaussian Elimination. 1.3 Matrices and Matrix Operations. 1.4 Inverses; Rules of Matrix Arithmetic. 1.5 Elementary Matrices and a Method for Finding A-1. 1.6 Further Results on Systems of Equations and Invertibility. 1.7 Diagonal, Triangular, and Symmetric Matrices. Chapter 2. Determinants. 2.1 Determinants by Cofactor Expansion. 2.2 Evaluating Determinants by Row Reduction. 2.3 Properties of the Determinant Function. 2.4 A Combinatorial Approach to Determinants. Chapter 3. Vectors in 2 Space and 3-Space. 3.1 Introduction to Vectors (Geometric). 3.2 Norm of a Vector; Vector Arithmetic. 3.3 Dot Product; Projections. 3.4 Cross Product. 3.5 Lines and Planes in 3-Space. Chapter 4. Euclidean Vector Spaces. 4.1 Euclidean n-Space. 4.2 Linear Transformations from Rn to Rm. 4.3 Properties of Linear Transformations from Rn to Rm. 4.4 Linear Transformations and Polynomials. Chapter 5. General Vector Spaces. 5.1 Real Vector Spaces. 5.2 Subspaces. 5.3 Linear Independence. 5.4 Basis and Dimension. 5.5 Row Space, Column Space, and Nullspace. 5.6 Rank and Nullity. Chapter 6. Inner Product Spaces. 6.1 Inner Products. 6.2 Angle and Orthogonality in Inner Product Spaces. 6.3 Orthonormal Bases: Gram-Schmidt Prodcess; QR-Decomposition. 6.4 Best Approximation; Least Squares. 6.5 Change of Basis. 6.6 Orthogonal Matrices. Chapter 7. Eigenvalues, Eigenvectors. 7.1 Eigenvalues and Eigenvectors. 7.2 Diagonalization. 7.3 Orthogonal Diagonalization. Chapter 8. Linear Transformations. 8.1 General Linear Transformations. 8.2 Kernel and range. 8.3 Inverse Linear Transformations. 8.4 Matrices of General Linear Transformations. 8.5 Similarity. 8.6 Isomorphism. Chapter 9. Additional topics. 9.1 Application to Differential Equations. 9.2 Geometry and Linear Operators on R2. 9.3 Least Squares Fit.

This classic treatment of linear algebra presents the fundamentals in the clearest possible way, examining basic ideas by means of computational examples and geometrical interpretation. It proceeds from familiar concepts to the unfamiliar, from the concrete to the abstract. Readers consistently praise this outstanding text for its expository style and clarity of presentation. The applications version features a wide variety of interesting, contemporary applications. Clear, accessible, step-by-step explanations make the material crystal clear. Established the intricate thread of relationships between systems of equations, matrices, determinants, vectors, linear transformations and eigenvalues.