This text for a second course in linear algebra, aimed at math majors and graduates, adopts a novel approach by banishing determinants to the end of the book and focusing on understanding the structure of linear operators on vector spaces. The author has taken unusual care to motivate concepts and to simplify proofs. For example, the book presents - without having defined determinants - a clean proof that every linear operator on a finite-dimensional complex vector space has an eigenvalue. The book starts by discussing vector spaces, linear independence, span, basics, and dimension. Students are introduced to inner-product spaces in the first half of the book and shortly thereafter to the finite- dimensional spectral theorem. A variety of interesting exercises in each chapter helps students understand and manipulate the objects of linear algebra. This second edition features new chapters on diagonal matrices, on linear functionals and adjoints, and on the spectral theorem; some sections, such as those on self-adjoint and normal operators, have been entirely rewritten; and hundreds of minor improvements have been made throughout the text.

Barron’s SAT Math Workbook provides realistic questions for all math topics on the SAT. This edition features: Hundreds of revised math questions with answer explanations Math strategies to help test-takers approach and correctly answer all of the question types on the SAT Answers and explanations for all questions This is an intensive preparation for the SAT's all-important Math section, and a valuable learning tool for college-bound students who may need extra help in math or who want to improve their math scores.

A groundbreaking introduction to vectors, matrices, and least squares for engineering applications, offering a wealth of practical examples.