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Vector Spaces, Matrices and Tensors in Physics
Authors:   M. C. Jain

ISBN: 978-81-8487-631-4 
Publication Year:   Reprint 2019
Pages:   296
Binding:   Paper Back


About the book

VECTOR SPACES, MATRICES AND TENSORS IN PHYSICS form an essential part of the mathematical background required by physicists. The book is written primarily as text book for the undergraduate and postgraduate students and as a reference book for working physicists. Special emphasis is given to topics relevant to physics, for example; linear independence and dependence of vectors, inner product, orthonormality, matrices as representations of linear transformations on vector spaces, similarity, eigenvalues, eigenvectors, diagonalization of matrices, expressing various physical quantities as tensors, tensorial formulation of vector algebra, calculus and geometry etc. the role of orthogonal, hermitian and unitary matrices in physics is highlighted.


Key Features

  • Key features: Solved problems are provided in each chapter Exercises with solutions/hints are provided at the end of the chapter Separate Appendix to understand the role of vector spaces and linear transformations in quantum mechanics Additional review problems with answers and hints are provided at the end of the book.



Table of content

Introduction/ Vector Spaces/ Linear Transformations/ Basic Matrix Algebra and Special Matrices/ Rank of Matrix/ Systems of Linear Equations/ Matrices and Linear Transformations/Eigenvalues and Eigenvectors of a matrix/ Caley-Hamilton Theorem, Minimal Polynomial of a Matrix/ Functions of a Matrix/ Bilinear, Quadratic, Hermitian and Skew-Hermitian Forms/ Cartesian Tensors/ Vector Algebra and Calculus using Cartesian Tensor/ Tensorial Formulation of Analytical Solid Geometry/ Tensorial Character of Some Physical Quantities/ General Tensors.




Audience
Undergraduate Students, Teachers and Researchers