“The Less is More Linear Algebra of Vector Spaces and Matrices” by Daniela Calvetti and Erkki Somersalo is a new textbook for a one semester proof-based undergraduate course of linear algebra. As the title suggests, the emphasis is from the beginning on vector spaces, and how linear operators represented in terms of matrices act on them. The treatise is compact and concise, focusing on the theoretical concepts rather than worked out examples. A particular feature of this book is the introduction of the singular value decomposition (SVD) early on so that the student sees the power of this decomposition both in analyzing the mapping properties of matrices as well as in terms of low rank approximations of matrices. This way, the SVD is seen as a fundamental property of every matrix rather than an afterthought of eigenvalue analysis. Similarly, Gaussian elimination is postponed towards the end of the course, thus avoiding to give the impression that matrices are just “tableaus of numbers” rather than fundamental objects characterized by how they transform vector spaces. The book is based on several years’ of experience of teaching linear algebra as part of the mathematics/applied mathematics program at CWRU.