Wellesley-Cambridge Press; 5th edition
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.