thank you... the Arxiv note is very relevant...robphy said:This may be helpful:
https://www.amazon.com/dp/0071756035/?tag=pfamazon01-20
http://arxiv.org/abs/math/0403252 (Quick introduction to tensor analysis by Sharipov)
Tensor notation is a mathematical language used to describe and manipulate tensors, which are mathematical objects that represent geometric quantities such as vectors and matrices. It is commonly used in physics and engineering.
Tensor notation is important because it allows for concise and elegant representation of complex mathematical concepts. It is also the standard notation used in many fields of science and engineering, making it essential for effective communication and understanding.
Tensor notation differs from other mathematical notations in that it uses index notation, where indices are used to represent the components of a tensor. This allows for compact representation of tensors with multiple dimensions, compared to other notations such as matrix notation.
Tensor notation is commonly used in fields such as physics, engineering, and computer science. It is particularly useful in areas such as general relativity, fluid mechanics, and image processing.
There are many resources available for learning tensor notation, including textbooks, online courses, and tutorials. It is recommended to have a strong foundation in linear algebra and multivariable calculus before diving into tensor notation. Practice and application of the notation is also crucial for mastery.