Elementary Linear Algebra

Elementary Linear Algebra
Bruce Cooperstein – University of California, Santa Cruz
ISBN10: 0988557207
ISBN13: 9780988557208
942 Pages
©2015 Worldwide Center of Mathematics
Digital PDF  $19.95 go > 
This is an etextbook for a first course in linear algebra. The topics covered include: Linear Systems, The Vector Space R^n, Matrix Algebra, Determinants, Abstract Vector Spaces, Linear Transformations, Eigenvalues and Eigenvectors, and Orthogonality in R^n. It introduces linear transformations in R^n quite early and uses them to motivate the addition and multiplication of matrices. In additional to the usual theory there are several sections devoted to applications such as Markov chain models, age structured population models, Leontief inputoutput models, errorcorrecting codes, linear recurrence relations, systems of differential equations, and the characterization of real quadratic curves and real quadratic surfaces. We also obtain the canonical forms for real 2 x 2 and 3 x 3 matrices.
The book is rigorous in its treatment of the theory and all important results are proved. What separates this book from print treatments of linear algebra and other etextbooks is the use of the digital environment to create a pedagogical product that supports student understanding. Specifically, without limitations of length we can regularly spiral back to important concepts and algorithms. Thus, each section begins with a subsection, “What you need to know” reviewing definitions and contains a short quiz with links to solutions. Also to facilitate student understanding, which depends on mastery of over 100 concepts, nearly every instance of a fundamental term is linked back to its definition. Likewise, in proofs, citation of previous results (lemmas, theorems, corollaries) are linked to their original statements and proofs. Also in each section there is a subsection. How to do it, where we describe the specific algorithms students will need to enact when assigned exercises. Further, in addition to a large selection of exercises, each section contains numerous challenge exercises (problems) which require knowledge of the theorems and the application of mathematical reasoning.