Linear Algebra What is a good textbook to start learning tensors?

[Feynman.12]

I am currently an undergraduate physics and applied mathematics student, and have wanted to go ahead in my course to learn about particle physics and general relativity. However, these topics, along with Quantum field theory which I want to learn about later, are taught in tensor notation. So Firstly, before i start studying these subjects, I will start tensors!

 

[RyanH42]

Schaum Tensor Calculus.
Schaum Vector Analysis
Schaum Differential Geometry
Here is the best options which I can recommend you

 

[Dr. Courtney]

https://en.wikipedia.org/wiki/Tensor

The wiki gives a good overview.

Many texts lose the forest for the trees.

 

[RyanH42]

https://www.physicsforums.com/threads/books-on-tensor-analysis.337824/
Or maybe this helps

 

[Fredrik]

Chapter 3 of "A first course in general relativity" by Bernard Schutz. I doubt that there's an easier introduction to the essential stuff about tensors. If you also read chapters 1-2, you will get the best intro to SR there is. I'm less enthusiastic about this book's treatment of GR. It's not mathematical enough for me.

Chapter 8 of "Linear algebra done wrong" by Sergei Treil. This is also the best book on linear algebra, so you will undoubtedly find the rest of the book very useful as well. It can be legally downloaded for free.

 

[vanhees71]

I was also inclined to suggest a GR book for intro to tensor analysis/differential geometry. However, there usually you find the treatment in terms of holonomic coordinates or the abstract coordinate free treatment, but usually only a minority of physics students need these ever in their lives and for sure not in the first semesters. There you usually need the classical vector analysis of 3D Euclidean space in Cartesian and orthonormal curvilinear coordinates. I've not found a book, where this is done in a way which completely satifies me, I must admit. A very good review is found in my favorite classical-physics books: A. Sommerfeld, Lectures on Theoretical Physics, vol. II (Fluid Dynamics).

Of the many books on GR, for my taste the best intro to this topic (in terms of the Ricci calculus in holonomic coordinates) is found in

H. Stephan, Relativity - An introduction to special and general relativity, 3rd edition, CUP 2004