May I say a little more, because many universities have not yet adjusted the balance toward linear algebra. But the scope of science and engineering and management (and life) is now so much wider, and linear algebra has moved into a central place. Certainly the laws of physics are well expressed by differential equations. Isaac Newton might not agree! But he isn’t teaching mathematics in the 21st century (and maybe he wasn’t a great teacher, but we will give him the benefit of the doubt). I personally believe that many more people need linear algebra than calculus. The questions are still a mixture of explain and compute-the two complementary approaches to learning this beautiful subject. I think you will approve of the extended choice of problems. Teaching for all these years required hundreds of new exam questions (especially with quizzes going onto the web). One step was certainly possible and desirable-to add new problems. This text was written to help our teaching of linear algebra keep up with the enormous importance of this subject-which just continues to grow. The spirit of the book could never change. So many people have read this book, and taught from it, and even loved it. Preface Revising this textbook has been a special challenge, for a very nice reason. A.5 The Kronecker Product A ⊗ B of Two Matricesĭ Glossary: A Dictionary for Linear Algebra A.4 The Tensor Product of Two Vector Spaces. A.3 The Cartesian Product of Two Vector Spaces. Ī Intersection, Sum, and Product of Spaces A.1 The Intersection of Two Vector Spaces. 8 Linear Programming and Game Theory 8.1 Linear Inequalities. 7.2 Matrix Norm and Condition Number 7.3 Computation of Eigenvalues. 7 Computations with Matrices 7.1 Introduction. 6 Positive Definite Matrices 6.1 Minima, Maxima, and Saddle Points 6.2 Tests for Positive Definiteness. 5.3 Difference Equations and Powers Ak 5.4 Differential Equations and eAt. ĥ Eigenvalues and Eigenvectors 5.1 Introduction. 3.4 Orthogonal Bases and Gram-Schmidt 3.5 The Fast Fourier Transform. Orthogonality 3.1 Orthogonal Vectors and Subspaces. 2.3 Linear Independence, Basis, and Dimension 2.4 The Four Fundamental Subspaces. Vector Spaces 2.1 Vector Spaces and Subspaces. 1.4 Matrix Notation and Matrix Multiplication 1.5 Triangular Factors and Row Exchanges. Matrices and Gaussian Elimination 1.1 Introduction. Linear Algebra and Its Applications Fourth Edition
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