Linear algebra and its applications / Gilbert Strang.

Includes index.

Matrices and Gaussian Elimination Introduction The Geometry of Linear Equations An Example of Gaussian Elimination Matrix Notation and Matrix Multiplication Triangular Factors and Row Exchanges Inverses and Transposes Special Matrices and Applications Review Exercises Vector Spaces Vector Spaces and Subspaces The Solution of m Equations in n Unknowns Linear Independence, Basis, and Dimension The Four Fundamental Subspaces Networks and Incidence Matrices Linear Transformations Review Exercises Orthogonality Perpendicular Vectors and Orthogonal Subspaces Inner Products and Projections onto Lines Least Squares Approximations Orthogonal Bases, Orthogonal Matrices, and Gram-Schmidt Orthogonalization The Fast Fourier Transform Review and Preview Review Exercises Determinants Introduction Properties of the Determinant Formulas for the Determinant Applications of Determinants Review Exercises Eigenvalues and Eigenvectors Introduction Diagonalization of a Matrix Difference Equations and the Powers Ak Differential Equations and the Exponential eAt Complex Matrices: Symmetric vs Hermitian Similarity Transformations Review Exercises Positive Definite Matrices Minima, Maxima, and Saddle Points Tests for Positive Definiteness The Singular Value Decomposition Minimum Principles The Finite Element Method Computations with Matrices Introduction The Norm and Condition Number The Computation of Eigenvalues Iterative Methods for Ax = b Linear Programming and Game Theory Linear Inequalities The Simplex Method Primal and Dual Programs Network Models Game Theory Computer Graphics The Jordan Form References Solutions to Selected Exercises Index

Renowned professor and author Gilbert Strang demonstrates that linear algebra is a fascinating subject by showing both its beauty and value. While the mathematics is there, the effort is not all concentrated on proofs. Strang's emphasis is on understanding. He explains concepts, rather than deduces. This book is written in an informal and personal style and teaches real mathematics. The gears change in Chapter 2 as students reach the introduction of vector spaces. Throughout the book, the theory is motivated and reinforced by genuine applications, allowing pure mathematicians to teach applied mathematics.

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