Items related to Vector Spaces, Matrices and Tensors in Physics
Synopsis
Vector spaces, matrices, and tensors in physics form an essential part of the mathematical background required by physicists. This book is written primarily as textbook for 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. The role of orthogonal, hermitian and unitary matrices in physics is highlighted.
Table of Contents
• 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.
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