Matrices and Tensors in Physics
By: A. W. Joshi
About This Book
This updated edition contains a good deal of new and relevant material including Bessel inequality, vector spaces of functions, physical laws and invariance principle, invariance in 3-D Newtonian and 4-D Minkowski spaces, fully antisymmetric tensors and their contraction. Discusses normal matrices and features a proof of the general theorem that a matrix posesses a complete set of orthonormal eigenvectors if and only if it is a normal matrix. Over 200 exercises and 100+ solved problems help students grasp the concepts presented.
AI Overview
"Matrices and Tensors in Physics" by A. W. Joshi is a comprehensive textbook that delves into the mathematical tools of matrices and tensors, focusing on their applications in physics. Here is a detailed overview of the book:
Key Themes
Introduction to Matrices:
- The book begins with an introduction to matrices through linear transformations on vector spaces. It covers the algebra of matrices, including special matrices, linear equations, and the eigenvalue problem.
Applications in Physics:
- The text highlights how matrices are used in solving systems of linear equations and eigenvalue problems. It also discusses specific matrices used in physics, such as rotation matrices, Pauli spin matrices, and Dirac matrices.
Infinite Matrices and Quantum Mechanics:
- A brief account of infinite matrices from the perspective of matrix formulation of quantum mechanics is included, emphasizing concepts like linear dependence and independence of vectors and matrices.
Tensors in Physics:
- The second chapter focuses on cartesian and general tensors. It discusses various physical situations requiring the use of second and higher rank tensors, such as effective mass tensor, moment of inertia tensor, stress, strain, and elastic constants. The Einstein summation convention is explained in detail, along with rules for checking the correctness of tensor equations.
Special Relativity and Electrodynamics:
- New sections on four-vectors in special relativity and covariant formulation of electrodynamics are included in this edition. This provides a broader context for the application of tensors in relativistic physics.
Parallel Displacement and Covariant Derivative:
- The book covers the concept of parallel displacement of vectors in Riemannian space and covariant derivative of tensors, leading to the curvature tensor and its properties.
Plot Summary
The book is structured to provide a systematic introduction to matrices and tensors, gradually increasing in complexity as it progresses. The first chapter lays the foundational concepts of matrices, while the second chapter delves deeper into tensors and their applications. The text is designed to be comprehensive, covering both theoretical foundations and practical applications in various areas of physics.
Critical Reception
While specific reviews are not provided in the sources, the book's inclusion in academic syllabi and its availability through multiple platforms suggest a positive reception among educators and students. The second edition's addition of new sections on special relativity and electrodynamics indicates an effort to keep the content relevant and up-to-date, which is often a criterion for academic success.
Availability
The book is available in paperback format through ThriftBooks for $8.89 and can be found on AbeBooks with an ISBN 9789386070906. It is also digitized and available on the Internet Archive, although access might be limited due to the archive's current status.
In summary, "Matrices and Tensors in Physics" by A. W. Joshi is a detailed textbook that provides a thorough understanding of matrices and tensors, emphasizing their applications in various areas of physics. Its comprehensive coverage and inclusion of new sections make it a valuable resource for students and educators alike.