Theory and Problems of Linear Algebra

Contents 1 Preliminary Concepts 2 Modules 3 Vector Spaces 4 Linear Transformations 5 Linear Transformations and Matrices 6 Determinants 7 Inner Product Spaces 8 Linear Operators on Inner Product Spaces 9 Unitary Spaces 10 Linear Operators on Unitary Spaces 11 Bilinear and Quadratic Forms IndexTheory and Problems of Linear Algebra has been designed to cater to the need of students opting Linear Algebra as a subject at undergraduate and postgraduate levels in various Indian universities The book exhaustively covers the subject matter and its applications in various fields To understand the subject matter covered in the book reader must be aware of some basic concepts of abstract algebra These prerequisites have been covered in Chapter-0 The reader is advised to go through this chapter first before switching over to the next chapter The subject matter has been graded in such a systematic manner that the knowledge of topics covered in each chapter except Chapter-0 is a prerequisite to understand the topics covered in the chapters to follow Chapter 1 deals with modules and emphasis has been given to module morphisms cyclic modules free modules and Notherian modules Chapter 2 is an extension of chapter 1 when ring is replaced by a field Linear independence and dependence of vectors have been discussed In Chapter 3 vector space homomorphisms widely known as linear transformation have been discussed Chapter 4 deals with relations between linear transformations between finite dimensional vector spaces and matrices In Chapter 5 concept of the determinant of a square matrix have been introduced and various properties of determinants have been discussed Inner product spaces unitary spaces and linear operators on them have been discussed in detail in the next four chapters Chapter 6 to Chapter 9 Bilinear forms and associated quadratic forms have been explained in the last chapter Features of the book will not only serve as a text book for a formal course in linear algebra but also as a supplement to standard texts in linear algebra and will also be helpful to all readers irrespective of their fields of specification 770 pp.…