Linear Algebra

●Introduces central topics, such as vector spaces, linear maps, linear dependence, and eigenvalues, early in the book with the aim of helping students transition from calculus to rigorous mathematics
●Motivates the reader whilst introducing new topics, definitions, and appropriate examples in connection with the core concepts presented early in the text so that students will be able to go back to these vital notions and, by the time the course ends, will have worked with them extensively
●Includes many pedagogical features, such as: 'Quick Exercises' throughout with answers upside-down at the bottom of the page; periodic 'Perspectives' that collect various viewpoints on particular topics developed throughout the text; and numerous in-text examples, end-of-chapter exercises, and hints and answers to selected problems at the end of the book

Elizabeth S. Meckes, Case Western Reserve University, Ohio
Elizabeth S. Meckes is Associate Professor at Case Western Reserve University, Ohio. Her research is in probability and analysis, with an emphasis on random matrix theory. She received her bachelor's (2001) and master's (2002) degrees at Case Western Reserve University, and her doctoral degree (2006) at Stanford University. She is currently writing a monograph on random matrices (Cambridge, forthcoming).

Mark W. Meckes, Case Western Reserve University, Ohio
Mark W. Meckes is Associate Professor at Case Western Reserve University, Ohio. His research is in analysis and probability, focusing on random matrix theory and metric geometry. He received his bachelor's (1999) and doctoral (2003) degrees at Case Western Reserve University, Ohio.

1. Linear systems and vector spaces
2. Linear maps and matrices
3. Linear independence, bases, and coordinates
4. Inner products
5. Singular value decomposition and the spectral theorem
6. Determinants