An Introduction To Linear Algebra
 ISBN: 9788120349520
 Author: MARWAHA, ALKA
 Number of Pages: 312
 Availability: In Stock
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About The Book An Introduction To Linear Algebra

Book Summary: 
This book is meant for an introductory course in linear algebra for undergraduate students of mathematics. It deals with the concept of vector spaces and special types of functions defined on them called linear transformations or operators. The vector spaces considered in the book are finitedimensional, a concept that involves representation of vectors in terms of a finite number of vectors which form a basis for the vector spaces. Written from a students perspective, this textbook explains the basic concepts in a manner that the student would be able to grasp the subject easily. Numerous solved examples and exercises given at the end of nearly each section will help the student to gain confidence in his/her analytical skills. What makes this book probably stand apart from other standard books on finitedimensional linear algebra is the introduction to Hilbert Space Theory. The generic model of a finitedimensional Hilbert space (real or complex) is IRn or sn but the true relevance of operators in Hilbert spaces surfaces only when they are infinitedimensional. In order to properly comprehend the structure of an infinitedimensional Hilbert space, it is important to grasp it at the finitedimensional level. Although finitedimensional Hilbert spaces are discussed comprehensively in the first eight chapters, it is only in the last three chapters that the treatment of Hilbert spaces is given in a setting which can be easily extended to defining infinitedimensional Hilbert spaces. After going through this textbook, the students will have a clear understanding of the model of a Hilbert space in finitedimensions and will then be able to smoothly make the transition to infinitedimensional Hilbert Space Theory. 
Table of Contents: 
Preface 1. Vector Spaces 2. Linear Transformations 3. Linear Functionals 4. Eigenvalues and Eigenvectors 5. Minimal Polynomials 6. Inner Product Spaces and Normed Linear Spaces 7. Adjoint of Linear Operators 8. Hilbert Spaces 9. Conjugate Hilbert Space 10. Projections on Hilbert Spaces 11. FiniteDimensional Spectral Theory Appendices 