Textbook in PDF format This book is chiefly designed for first-year university students and instructors studying or teaching a fundamental linear algebra course. It offers a thorough introduction to linear algebra, organized into chapters that cover essential topics, from basic concepts to more advanced applications, with a focus on solved exercises for effective learning. The structure of the book includes four main sections in each chapter: Course Summary, True or False, Exercises with Solutions, and Exercises without Solutions. The book’s design ensures that students can build their understanding progressively. Detailed solutions help reinforce the material, while the True or False section promotes critical thinking. Notice that while the majority of the questions in this section are framed as true or false, there are instances where certain questions do not have a simple binary answer. Some questions may require further exploration, where different cases or scenarios need to be discussed, depending on the context. Exercises without solutions encourage independent problem-solving, giving students the tools they need to assess their understanding and readiness for exams. This combination of theory, application, and self-assessment makes the book an ideal resource for both classroom learning and self-study. Introduction. Matrices. Vector Spaces. Linear Maps on Vector Spaces. Determinants and Systems of Linear Equations. Special Matrices. Eigenvalues. Diagonalization and Triangularization. Positive Semi-definite Matrices on M2 (R). Bibliography. Index