Linear algebra: concepts and methods

"Any student studying linear algebra will welcome this textbook, which provides a thorough, yet concise, treatment of key topics in university linear algebra courses. Blending practice and theory, the book enables students to practice and master the standard methods as well as understand how they actually work. At every stage the authors take care to ensure that the discussion is no more complicated or abstract than it needs to be, and focuses only on the fundamental topics. Hundreds of examples and exercises, including solutions, give students plenty of hands-on practice End-of-chapter sections summarise material to help students consolidate their learning Ideal as a course text and for self-study Instructors can use the many examples and exercises to supplement their own assignments Both authors have extensive experience of undergraduate teaching and of preparation of distance learning materials"--

Cover -- Linear Algebra: Concepts and Methods -- Title -- Copyright -- Dedication -- Contents -- Preface -- Preliminaries: before we begin -- Sets and set notation -- Numbers -- Mathematical terminology -- Basic algebra -- Algebraic manipulation -- Powers -- Quadratic equations -- Polynomial equations -- Trigonometry -- A little bit of logic -- 1 Matrices and vectors -- 1.1 What is a matrix? -- 1.2 Matrix addition and scalar multiplication -- 1.3 Matrix multiplication -- 1.4 Matrix algebra -- 1.5 Matrix inverses

1.5.1 The inverse of a matrix1.5.2 Properties of the inverse -- 1.6 Powers of a matrix -- 1.7 The transpose and symmetric matrices -- 1.7.1 The transpose of a matrix -- 1.7.2 Properties of the transpose -- 1.7.3 Symmetric matrices -- 1.8 Vectors in Rn -- 1.8.1 Vectors -- 1.8.2 The inner product of two vectors -- 1.8.3 Vectors and matrices -- 1.9 Developing geometric insight -- 1.9.1 Vectors in R2 -- 1.9.2 Inner product -- 1.9.3 Vectors in R3 -- 1.10 Lines -- 1.10.1 Lines in R2 -- 1.10.2 Lines in R3 -- 1.11 Planes in R3

1.12 Lines and hyperplanes in Rn1.12.1 Vectors and lines in Rn -- 1.12.2 Hyperplanes -- 1.13 Learning outcomes -- 1.14 Comments on activities -- 1.15 Exer…