Most helpful positive review
5.0 out of 5 starsExcellent introduction to Linear Algebra
ByRogelio Trujilloon July 20, 2001
This is an Excellent book, and also [a] very [good value] for their quality (I will never understand the reason for which other books, bad some of them, reach prices so high presenting topics that are treated by other books so [very good value] as this, and that they present the topics in excellent form). Comparing it with the book of Mirsky I encounter substantial differences, although the content characteristic of the linear algebra doesn't change. It treats the determinant defining them in a single formula and once and for all. Mirsky makes it defining the whole content of the theory of Silvester, more enriched, more substantial. Shilov extends the theory of the determinant along the book, while Mirsky makes it in a single chapter dedicated to its study. Mirsky conserves along the whole book, a classic presentation of the lineal algebra, while Shilov tries to enrich the topic introducing elements of modern algrebra. Mirsky has more exercises at the end of each chapter and they don't have answer, Shilov includes less, but it has answers to the exercises at the end of his book. Considering Mirsky my favorite one, I give a very special place to Shilov since he gives you a wider panorama and you terminate locating the lineal Algebra in a wider context inside the mathematics (definition of Algebras and a very good introduction to the algebra of the polinomiales, introduction to the tensorial algebra etc). This book is for an intermediate level, for undergraduates, and I recommend it to anyone that wants to study the linear algebra having the security that the concepts will be very clear. Their reading is easy to continue and it is a good introduction to the abstract algebra.