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 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.

'This is a book for anyone who wants to really understand linear algebra. Instead of mere cookbook recipes or dry proofs, it provides explanations, examples, pictures - and, yes, algorithms and proofs too, but only after the reader is able to understand them. And while it is aimed at beginners, even experts will have something to learn from this book.' John Baez, University of California, Riverside

• 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.