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.
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