inear Algebra, with Applications Eight Edition

Abstract

T hist.ext is an introduction t.o Linear Algebra suitable for a course usually offered at the sophomore level. The .materlal is manged in three parts. Part 1 consists of what I regard as basic mat.erial-discussions of systems of linear equations, veer.ors in Rn (including the concepts of linear combination, basis, and dimension), mattices, linear transformations, determinants, eigenvalues, and eigenspaces, as well as optional applicati.ons. Part 2 builds on this material t.o discuss general vector spaces, such as spaces of matiicoordinate ces and functions. It includes topics such as 1he rank/nullity 1heorem. inner products, and .representations. Part 3 completes the course wi1h some of the important ideas and methods in Numerical Linear Algebra such as ill-conditioning, pivoting, LU decomposition, and Singular Value Decomposition. This edition continues the tradition of earlier editions by being a flexible blend of theory, important numerical techniques, and interesting applications. The book is arranged ductory around 29 core sections. These sections include topics that I think are essential t.o an introlinear algebra course. There is then ample time for the instructor to select further topics that give the course the desired flavor. Eighth Edition The arrangement of topics is the same as in the Seventh Edition. The vect.or space R", subspaces, bases, and dimension are introduced early (Chapter 1), and are then used in a natural, gradual way to discuss such concepts as linear transformations in R" (Chapter2) and eigenspaces (Cliapter 3), leading to general vector spaces (Chapter 4). 'Ihe level of abstraction gradually increases as one progresses in the course-and the big jump that often exists for students in going from maJrix algebra to general vector spaces is no longer there. The first three chapters give the foundation of 1he vector space R11; they really form a fairly complete elementary minicourse for the vector space Rn. The rest of the course builds on this solid foundation. Changes This edition is a refinement of the Seventh Edition. Certain sections have been rewritten. others added, and new exercises have been included. The aim has been to improve example, the clarity, flow, and selection of material. The discussion of projections in Section 4.6, for has been rewritten. The proof of the Gram-Schmidt Orthogonali7.ation process