Gilbert Strang’s textbooks have changed the entire approach to learning linear algebra — away from abstract vector spaces to specific examples of the 4 fundamental subspaces: the column space and nullspace of A and A’.
Strang’s new Introduction to Linear Algebra, 5th edition, (PDF) has become more than a textbook for the basic linear algebra course. That is its first purpose and always will be. The new chapters about applications of the SVD, probability, and statistics, and Principal Component Analysis in finance and genetics make it also a textbook for a second course, plus a resource at work. Linear algebra has become central in modern applied mathematics. This ebook supports the value of understanding linear algebra.
Introduction to Linear Algebra, 5e includes challenge problems to complement the review problems that have been highly praised in previous editions. The basic course is followed by 8 applications: graphs and networks, differential equations in engineering, Fourier methods and the FFT, statistics, computer graphics, linear programming, Principal Component Analysis, cryptography, and singular values.
Audience: Thousands of teachers in universities and colleges and now even high schools are using this ebook, which truly explains this crucial subject. This textbook is for students everywhere, with support from the websites and video lectures. Each chapter begins with a summary for efficient review.
Contents: Chap. 1: Introduction to Vectors; Chap. 2: Solving Linear Equations; Chap. 3: Vector Spaces and Subspaces; Chap. 4: Orthogonality; Chap. 5: Determinants; Chap. 6: Eigenvalues and Eigenvectors; Chap. 7: Singular Value Decomposition; Chap. 8: Linear Transformations; Chap. 9: Complex Vectors and Matrices; Chap. 10: Applications; Chap. 11: Numerical Linear Algebra; Chap. 12: Linear Algebra in Probability and Statistics; Matrix Factorizations; Index; Six Great Theorems.
First, let us consider the ebook itself. As with his classic Linear Algebra and its Applications (Academic Press) from 40 ago, Strang’s latest new 5th edition of Introduction to Linear Algebra keeps one eye on the theory, the other on applications, and has the stated goal of “opening linear algebra to the world” (Preface, page x). Aimed at the serious undergraduate student – though not just those undergraduates who fill the lecture halls of MIT, Strang’s home institution – the writing is personal and engaging, and the presentation is exceptionally informative and clear (even seasoned instructors may benefit from Strang’s insights). The first 6 chapters offer a traditional first course that covers systems of linear equations, vector algebra and geometry, vector spaces and subspaces, determinants, orthogonality, and eigenvalues and eigenvectors. The next 3 chapters are devoted to the singular value decomposition, linear transformations, and complex numbers and complex matrices followed by chapters that address a wide range of contemporary applications and computational issues. The ebook concludes with a brief but cogent treatment of linear statistical analysis.
NOTE: This sale only includes Linear Algebra and its Applications 5th edition in PDF. No online access codes included.