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 summarize 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"--

Includes index.

Preliminaries : before we begin -- Sets and set notation -- Numbers -- Mathematical terminology -- Basic algebra -- Trigonometry -- A little bit of logic -- 1. Matrices and vectors -- what is a matrix? -- Matrix addition and scalar multiplication -- Matrix multiplication -- Matrix algebra -- Matrix inverses -- Powers of a matrix -- The transpose and symmetric matrices -- Vectors -- Developing geometric insight -- Lines -- Planes -- Lines and hyperplanes -- 2. Systems of linear equations -- Row operations -- Gaussian elimination -- Homogeneous systems and null space -- 3. Matrix inversion and determinants -- Matrix inverse using row operations -- Determinants -- Matrix inverse using cofactors -- Leontief input-output analysis -- 4. Rank, range and linear equations -- Rank of a matrix -- Rank and systems of linear equations -- Range -- 5. Vector spaces -- Subspaces -- Linear span -- 6. Linear independence, bases and dimension -- Linear independence -- Bases -- Coordinates -- dimension -- Basis and dimension -- 7. Linear transformations and change of basis -- Range and null space -- Coordinate change -- Change of basis and similarity -- 8. Diagonalisation -- Eigenvalues and eigenvect…