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

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.

Over 300 unusual problems, ranging from easy to difficult, involving equations and inequalities, Diophantine equations, number theory, quadratic equations, logarithms, more. Detailed solutions, as well as brief answers, for all problems are provided.

Publisher's Note: Products purchased from Third Party sellers are not guaranteed by the publisher for quality, authenticity, or access to any online entitlements included with the product. Learn Algebra quickly and easily! Must Know High School Algebra is more than just an Algebra workbook. Its user-friendly format and concept-first approach give you the edge you need now to improve your Algebra skills for homework, classwork, and exams. It's like a lightning bolt to the brain! As part of our Must Know series, Must Know High School Algebra provides a fresh approach to learning by making sure what you really need to know is clear up-front. Chapters begin with the must know ideas, or concepts. The chapter then shows you how these important concepts will help you succeed in your studies. Plenty of examples, clear answer explanations, and practical exercises at the end of each chapter help boost your confidence that you've mastered the essential topics. Dive into this book and find: • 400+ practice questions that mirror what you will find in your classwork and on exams • A bonus app with 100+ flashcards that will reinforce what you’ve learned • An easy-access setup that allows you to jump in and out of subjects • Algebra topics aligned to national and state education standards • Conversational writing style and informative sidebars for much needed support • Special help for more challenging algebra subjects, including linear inequalities, quadratic functions, and radical expressions