Any good books on tensors/multilinear algebra?

[bda23]

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.

 

[krome]

An Introduction to Tensors and Group Theory for Physicists by Nadir Jeevanjee.

 

[Alesak]

Try A Student's Guide to Vectors and Tensors, it has very good reviews. I did not read it personaly, but intend to do so soon.

 

[alissca123]

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!)

 

[bda23]

Thanks everyone, those books don't look too bad.

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?

 

[alissca123]

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.