Any good books on tensors/multilinear algebra?

In summary, the conversation is about finding a suitable book on tensors for someone with a background in linear algebra and real analysis, but is more interested in the applications in mechanics rather than the purely mathematical aspect. The ideal book would have modern notation and a focus on general tensors, not just Cartesian, with some differential geometry applications. It should also be geared towards applied mathematicians, physicists, and engineers rather than pure mathematicians. Several book recommendations were given, including An Introduction to Tensors and Group Theory for Physicists by Nadir Jeevanjee and A Student's Guide to Vectors and Tensors. The conversation also mentions Tensor Analysis on Manifolds by Bishop, which is described as a rigorous book with a focus on abstract algebra
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I have been dealing with tensors for quite a few years, working my way through a good number of different books on tensors. However, I keep getting frustrated at times at the low quality of many books. I have a good background in linear algebra and some real analysis, but I am not interested in tensors as a purely mathematical construct, but for applications in mechanics. What I am looking for would ideally include the following:

- some modern notation and orientation towards linear algebra. Not just the old component-based approach, which seems more like an exercise in algebraic manipulation, without gaining any understanding
- general tensors, not just Cartesian, ideally with some differential geometry applications
- not geared primarily towards mathematicians, as my knowledge of analysis is not quite good enough. Rather oriented towards applied mathematicians, physicists, engineers, i.e. not an entire book just listing theorems and proofs (they have to be included to some extent, of course, but not making up 100% of the content)
- perhaps some differential forms, but this is really not essential

Does anyone know of a suitable book? Thanks.
 
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An Introduction to Tensors and Group Theory for Physicists by Nadir Jeevanjee.
 
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Thanks everyone, those books don't look too bad.

alissca123 said:
Have you tried Tensor Analysis on Manifolds by Bishop?
https://www.amazon.com/dp/0486640396/?tag=pfamazon01-20
I think it's a nice book (plus, it's Dover!)

I've heard of the book, but was unsure whether it was too theoretical/geared towards pure mathematicians. Would you say it also helps to develop some intuitive feeling/geometric view of tensors or is it rather leaning towards abstract algebra?
 
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Well, the book is rigorous... and there are almost no diagrams, but I think it is very very clear (plus it's Dover! haha)
The final chapter is applications to mechanics.
 

1. What is the best book for beginners on tensors and multilinear algebra?

For beginners, "Tensor Calculus for Physics: A Concise Guide" by Dwight E. Neuenschwander is a great choice. It covers the basics of tensors and multilinear algebra in a clear and concise manner with plenty of examples and exercises.

2. Are there any books that cover tensors and multilinear algebra in a more advanced manner?

Yes, "Tensors, Differential Forms, and Variational Principles" by David Lovelock and Hanno Rund is a highly recommended text for advanced study. It delves into the geometric and differential aspects of tensors and multilinear algebra.

3. Is there a book that focuses specifically on applications of tensors and multilinear algebra?

"Applications of Tensor Analysis" by A.J.M. Spencer is a great resource for those interested in the practical applications of tensors and multilinear algebra. It covers topics such as elasticity, continuum mechanics, and general relativity.

4. Can you recommend a book that is suitable for self-study?

"Tensor Algebra and Tensor Analysis for Engineers: With Applications to Continuum Mechanics" by Mikhail Itskov is a self-contained text that is suitable for self-study. It provides a thorough introduction to tensors and multilinear algebra with a focus on engineering applications.

5. Are there any online resources for learning about tensors and multilinear algebra?

Yes, "Introduction to Tensor Calculus and Continuum Mechanics" by John H. Heinbockel is a free online textbook that covers the fundamentals of tensors and multilinear algebra. There are also various lecture notes and video lectures available on sites like YouTube and Coursera.

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