The aim of this book is two-fold: to introduce the fundamental concepts of linear algebra and to apply the theorems in computation-oriented applications. The book is suitable for a one semester coursein linear algebra that can be used in a variety of contexts. The presentationof the material combines definitions and proofs with an emphasis oncomputational applications, providing examples that illustrate the use ofsoftware packages such as Mathematica®,Maple®, and Sage. Features: - Introduces the fundamental concepts of linear algebra and applies the theorems in computation-oriented applications - Presents a brief introduction of some aspects of abstract algebra that relate directly to linear algebra, such as groups, rings, modules, fields and polynomials over fields.
However the book is logically self-contained. In this new edition, many parts of the book have been rewritten and reorganized, and new exercises have been added.
Numerical Linear Algebra is a concise, insightful, and elegant introduction to the field of numerical linear algebra.
Covers determinants, linear spaces, systems of linear equations, linear functions of a vector argument, coordinate transformations, the canonical form of the matrix of a linear operator, bilinear and quadratic forms, Euclidean spaces, ...
Line up the basics — discover several different approaches to organizing numbers and equations, and solve systems of equations algebraically or with matrices Relate vectors and linear transformations — link vectors and matrices with ...
"This book is intended for first- and second-year undergraduates arriving with average mathematics grades ... The strength of the text is in the large number of examples and the step-by-step explanation of each topic as it is introduced.
But this follows immediately from the Cauchy—Schwartz inequality, which can be stated as cos6 : (X. y) llXll llyll Definition 10.9 (Orthogonal vectors) Suppose that V is an inner. The usefulness of this definition is in the concept of ...
While not designed as an introductory text, the book's well-chosen topics, brevity of presentation, and the author's reputation will recommend it to all students, teachers, and mathematicians working in this sector.
In short, this is material that many of us wish we had been taught as graduate students. Roughly the first third of the book covers the basic material of a first course in linear algebra.
One of the best available works on matrix theory in the context of modern algebra, this text bridges the gap between ordinary undergraduate studies and completely abstract mathematics. 1952 edition.
A groundbreaking introduction to vectors, matrices, and least squares for engineering applications, offering a wealth of practical examples.