- #1
Mothrog
- 22
- 0
I wonder if anyone might have some suggestions for a good self-study book on tensors. I'm just starting in on Jackson and have only seen tensors briefly in my previous undergrad classes. Any suggestions?
mathwonk said:i like Foundations of Differentiable Manifolds and Lie Groups
by Frank Warner
A tensor is a mathematical object that describes the relationship between vectors and scalars in a multi-dimensional space. It can be thought of as a generalization of a vector, which only describes magnitude and direction, to higher dimensions.
While both tensors and matrices are multi-dimensional arrays of numbers, they serve different purposes. Tensors can operate on multiple vectors and scalars simultaneously, whereas matrices can only operate on one vector at a time. Tensors also have additional properties, such as rank and order, that matrices do not have.
Tensors have a wide range of applications in fields such as physics, engineering, and machine learning. They are used to describe physical quantities, such as stress and strain in materials, and to model complex systems, such as neural networks in deep learning.
While a basic understanding of linear algebra and calculus is helpful, it is not necessary to have a strong background in math to learn tensors. The concepts can be understood through visualizations and practical examples, and there are many resources available for self-study.
This book is designed for self-study, but having a teacher or mentor can be helpful in clarifying any questions or difficulties that may arise. It is recommended to have a basic understanding of linear algebra before starting to learn tensors on your own.