Название: Matrices and Linear Algebra with GAP Автор: Akhilesh Chandra Yadav Издательство: Educreation Publishing Год выхода: 2020 Страниц: 377 Формат: True PDF Размер: 15,9 MB Язык: английский
The purpose to write this book is to provide a textbook of basic Linear Algebra course at all Universities. Therefore it is written according to the unified syllabus of Indian universities to fulfil the requirements of un dergraduate students. We have written this book through a computational approach. Indeed, our main purpose of writing this book is to improve the computational skill of undergraduate students and to update them with the mathematical software GAP “Group Algorithm and Packages”. GAP commands are provided with each topic where it is necessary. To inculcate students, each section is equipped with solved examples and exercises. We have not given answer to the questions for assignment purposes.
This book is divided into ten chapters. First five chapters deal the course on matrices and the rest deal the course on Linear Algebra. In Chapter 1, the notion of matrices and their operations are given. Some particular type of matrices like Symmetric, Skew-Symmetric, Hermitian, Skew-Hermitian, Orthogonal and Unitary are discussed here. In Chapter 2, the notion of determinant of square matrices are discussed. In this chapter we have also introduced Cramer’s rule for finding the solution of a system of linear equations. In the Chapter 3, the notion of ranks of matrices and the reductions of matrices into Echelon and Normal forms, are given. The method of finding inverse of non-singular square matrices using elementary operations are also given. The Chapter 4 deals the consistency and inconsistency of system of linear equations. The application of ranks and echelon forms in finding the solution of system of linear equations are also given. The Chapter 5 deals the notion of eigenvalues, eigenvectors are given. The nature of eigen vectors and their role in the diagonalization of square matrices are discussed. The application of Cayley-Hamilton’s theorem is also given. The chapter 6 deals the abstract notion of vector spaces, subspaces and quotient spaces. The chapter 7 deals the study of linear transformations and linear functionals. In the Chapter 8, the matrix connection of linear transformations and the effect of change of basis on the matrix of linear transformations, are given. The Chapter 9 deals inner product spaces. The last chapter deals the notion of bilinear forms and quadratic forms. Method of installation of GAP is given in Appendix.
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Matrices and Linear Algebra with GAP 
Название: Matrices and Linear Algebra with GAP