Bibliothèque de L'IMIST/CNRST

Preface -- Linear Phenomena and Euclidean Spaces of Small Dimension -- Concrete Vector Spaces -- Vector Spaces and Subspaces -- Linear Transformations -- More Matrix Algebra and Determinants -- General Theory of Linear Equations -- Eigenvectors -- Orthogonality -- Forms -- Vector Spaces over Finite Fields -- Appendix A: Complex Numbers -- Appendix B: Polynomials over Complex Numbers -- References -- Index.                                                                                                                                     .

This textbook provides a rigorous introduction to linear algebra in addition to material suitable for a more advanced course while emphasizing the subject’s interactions with other topics in mathematics such as calculus and geometry. A problem-based approach is used to develop the theoretical foundations of vector spaces, linear equations, matrix algebra, eigenvectors, and orthogonality. Key features include: • a thorough presentation of the main results in linear algebra along with numerous examples to illustrate the theory;  • over 500 problems (half with complete solutions) carefully selected for their elegance and theoretical significance; • an interleaved discussion of geometry and linear algebra, giving readers a solid understanding of both topics and the relationship between them.   Numerous exercises and well-chosen examples make this text suitable for advanced courses at the junior or senior levels. It can also serve as a source of supplementary problems for a sophomore-level course.     .