Tensors are mathematical objects that describe the relationship between vectors and scalars in a multi-dimensional space. They are important because they are used to represent physical quantities and describe the behavior of physical systems, making them essential in many areas of science and engineering.
A good intro book on tensors should provide a clear and concise explanation of the fundamental concepts, as well as practical applications in various fields. It should also include exercises and examples to help readers understand and apply the concepts.
While a basic understanding of linear algebra and calculus is helpful, a good intro book on tensors should provide a comprehensive and accessible explanation of the concepts, making it suitable for readers with varying levels of mathematical background.
Yes, tensors have applications in various fields such as engineering, computer science, and data analysis. They can be used to model and analyze complex systems and relationships in these fields.
Yes, there are many online resources and textbooks available for further study on tensors, such as "Tensor Calculus for Physics" by Dwight E. Neuenschwander and "Tensor Analysis and Elementary Differential Geometry for Physicists and Engineers" by Hung Nguyen-Schäfer. It is also helpful to explore applications of tensors in specific fields, such as machine learning or general relativity.