Linear Algebra

The book is an introduction to linear algebra intended as a textbook for the first course in linear algebra. In the first six chapters we present the core topics: matrices, the vector space ℝn, orthogonality in ℝn, determinants, eigenvalues and eigenvectors, and linear transformations. The book gives students an opportunity to better understand linear algebra in the next three chapters: Jordan forms by examples, singular value decomposition, and quadratic forms and positive definite matrices.In the first nine chapters everything is formulated in terms of ℝn. This makes the ideas of linear algebra easier to understand. The general vector spaces are introduced in Chapter 10. The last chapter presents problems solved with a computer algebra system. At the end of the book we have results or solutions for odd numbered exercises.Contents: MatricesThe Vector Space ℝnOrthogonality in ℝnDeterminantsEigenvalues and EigenvectorsLinear TransformationsJordan Forms by ExamplesSingular Value DecompositionQuadratic Forms and Positive Definite MatricesVector SpacesSolutions with CASAnswers to Selected Exercises
Readership: Undergraduate students taking a first course in linear algebra.Linear Algebra;Matrix;Vector;Determinant;System of Equations;Orthogonal;Eigenvalue;Eigenvector;Diagonalization;Rotations;Gauss Elimination;Geometry;Linear Independence;Singular Value Decomposition;Quadratic Forms;Linear Transformations;Vector Spaces;Dot Product;Cross Product0Key Features:The book has a chapter with examples of Jordan forms, which is rare in textbooks for a first course in linear algebra. Students will be better prepared for a second course in linear algebra where Jordan forms play an important roleThe book uses a computer algebra system not only to facilitate calculations, but also to improve understanding of linear algebraThe book has a comprehensive companion book where we present, in a style consistent with the present book, particular cases of all important results from this book. Students can read all chapter they are interested in or parts of it when they find the general case too abstractMost of our proofs are elementary and easy to read. To this end we use in our proofs, whenever possible, the Gauss elimination method and properties of inverse matrices