Review of Linear Algebra and its Applications by D.C. Lay

The most obvious benefit of this particular book is its size. At fewer than five hundred pages it is a comparatively light book. Despite its compact nature, it does include some clear and helpful illustrations, and features some interesting applications
However, the layout is far from appealing, and at first glance can be confusing. The answers to the random exercises can be difficult to locate, and the solutions are often too brief to be of any use. In general the proofs are difficult to follow because they are in compact notation, and like many books of this type, it makes little provision for students struggling to remember previously mentioned results and definitions. In some cases a theorem is stated on page X and then the proof of this theorem is given on page X+2 without restating the theorem. This means the reader is constantly flicking between pages X and X+2. The inclusion of repeated theorems would not hamper the confident mathematician, but would be invaluable to a less self assured student.
There seems to be little attempt made to inspire the reader, and its approach is largely clinical and less personal.