A Bridge to Linear Algebra
- Length: 508 pages
- Edition: 1
- Language: English
- Publisher: WSPC
- Publication Date: 2019-03-12
- ISBN-10: 981120022X
- ISBN-13: 9789811200229
- Sales Rank: #5941686 (See Top 100 Books)
The book makes a first course in linear algebra more accessible to the majority of students and it assumes no prior knowledge of the subject. It provides a careful presentation of particular cases of all core topics. Students will find that the explanations are clear and detailed in manner. It is considered as a bridge over the obstacles in linear algebra and can be used with or without the help of an instructor.
While many linear algebra texts neglect geometry, this book includes numerous geometrical applications. For example, the book presents classical analytic geometry using concepts and methods from linear algebra, discusses rotations from a geometric viewpoint, gives a rigorous interpretation of the right-hand rule for the cross product using rotations and applies linear algebra to solve some nontrivial plane geometry problems.
Many students studying mathematics, physics, engineering and economics find learning introductory linear algebra difficult as it has high elements of abstraction that are not easy to grasp. This book will come in handy to facilitate the understanding of linear algebra whereby it gives a comprehensive, concrete treatment of linear algebra in R² and R³. This method has been shown to improve, sometimes dramatically, a student’s view of the subject.
Contents Preface 1 Basic ideas of linear algebra 1.1 2 x 2 matrices 1.2 Inverse matrices 1.3 Determinants 1.4 Diagonalization of 2 x 2 matrices 2 Matrices 2.1 General matrices 2.2 Gaussian elimination 2.3 The inverse of a matrix 3 The vector space R2 3.1 Vectors in R2 3.2 The dot product and the projection on a vector line in R2 3.3 Symmetric 2 x 2 matrices 4 The vector space R3 4.1 Vectors in R3 4.2 Projections in R3 5 Determinants and bases in R3 5.1 The cross product 5.2 Calculating inverses and determinants of 3 x 3 matrices 5.3 Linear dependence of three vectors in R3 5.4 The dimension of a vector subspace of R3 6 Singular value decomposition of 3 x 2 matrices 7 Diagonalization of 3£3 matrices 7.1 Eigenvalues and eigenvectors of 3 x 3 matrices 7.2 Symmetric 3 x 3 matrices 8 Applications to geometry 8.1 Lines in R2 8.2 Lines and planes in R3 9 Rotations 9.1 Rotations in R2 9.2 Quadratic forms 9.3 Rotations in R3 9.4 Cross product and the right-hand rule 10 Problems in plane geometry 10.1 Lines and circles 10.2 Triangles 10.3 Geometry and trigonometry 10.4 Geometry problems fromthe International Mathematical Olympiads 11 Problems for a computer algebra system 12 Answers to selected exercises Bibliography Index
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