Linear Algebra and its Applications, Global Edition
About the TextbookEarly introduction of key concepts: Fundamental ideas of linear algebra are introduced within the first seven lectures, in the concrete setting of Rn, then gradually examined from different points of view. Later, generalisations of these concepts appear as natural extensions of familiar ideas. Linear transformations form a “thread” that is woven into the fabric of the text. Their use enhances the geometric flavor of the text. In Chapter 1, for instance, linear transformations provide a dynamic and graphical view of matrix-vector multiplication. Orthogonality and Least-Squares Problems receive more comprehensive treatments than is commonly found in beginning texts because orthogonality plays such an important role in computer calculations and numerical linear algebra and because inconsistent linear systems arise so often in practical work. Eigenvalues appear fairly early in the text, in Chapters 5 and 7. Because this material is spread over several weeks, students have more time to absorb and to review these critical concepts. Eigenvalues are motivated by and applied to discrete and continuous dynamical systems, which appear in Sections 1.10, 4.8, and 4.9, and in five sections of Chapter 5. A modern view of matrix multiplication is presented, with definitions and proofs focusing on the columns of a matrix rather than on the matrix entries. Focus on visualisation of concepts throughout the book helps students grasp the concepts.Each major concept in the course is given a geometric interpretation because many students learn better when they can visualise an idea. Numerical Notes provide a realistic slant to the text. Students are reminded frequently of issues that arise in real-life applications of linear algebra. Applications are varied and relevant. Some applications appear in their own sections; others are treated within examples and exercises. Each chapter opens with an introductory vignette that sets the state for some applications of linear algebra and provides a motivation for developing the mathematics that follows. Exercise sets are meticulously constructed and consist of the following elements. Each section features an abundant supply of exercises, ranging from routine computations to conceptual questions to applications. Innovative questions pinpoint conceptual difficulties that the authors have found in student papers over the years. A few carefully selected Practice Problems appear just before each exercise set. Complete solutions follow the exercise set. These problems either focus on potential trouble spots in the exercise set or provide a “warm-up” for the exercises, and the solutions often contain helpful hints or warnings about the homework. True/False Questions appear just after the computational exercises and encourage students to read the text and think critically. NEW! Conceptual Practice Problems and their solutions in most sections provide proof- or concept-based examples for students to review. [M] exercises appear in every section. To be solved with the aid of a [M]atrix program such as MATLAB™, Maple®, Mathematica®, MathCad®, Derive® or programmable calculators with matrix capabilities, such as the TI-83 Plus®, TI-86®, TI-89®, and HP-48G®. Data for these exercises are provided on the Web.
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