Linear algebra (Q5947993)

Designed as a 2-semester course for students with some background of elementary algebra (vectors, linear equations,\dots), this carefully written book gives a thorough account of the basic ideas of linear algebra. Its scope is indicated by the 7 chapter headings: vector spaces, linear mappings, matrices, determinants, polynomials, (similarity) normal forms, Euclidean and unitary spaces. Most students find abstract algebra daunting at first encounter. The author's policy is to preface each chapter with an informal ``motivating'' section but thereafter to develop the material rigorously and in full generality. For example, the basis theorem for finite dimensional vector spaces over an arbitrary field is proved in chapter 1, groups, fields and vector spaces being defined on the way. The student who enters into the spirit of the book will be rewarded but will have to work hard. The treatment is along traditional lines with a few exceptions. Determinants are introduced in the spirit of exterior algebra and there is an optional section on exterior products. Normal forms for matrices are derived via the theory of modules over a principal ideal domain. The book is abundantly provided with exercises.