Any good books on tensors/multilinear algebra?

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Discussion Overview

The discussion revolves around recommendations for books on tensors and multilinear algebra, particularly focusing on their applications in mechanics rather than purely mathematical constructs. Participants express their preferences for modern notation, accessibility for applied mathematicians, and the inclusion of differential geometry concepts.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested

Main Points Raised

  • One participant expresses frustration with the quality of existing tensor books and outlines specific criteria for a suitable book, including modern notation and a focus on applications in mechanics.
  • Another participant recommends "An Introduction to Tensors and Group Theory for Physicists" by Nadir Jeevanjee.
  • A suggestion is made for "A Student's Guide to Vectors and Tensors," noted for its positive reviews, although the recommender has not yet read it.
  • "Tensor Analysis on Manifolds" by Bishop is mentioned as a potential resource, with a link provided for reference.
  • One participant questions whether Bishop's book is too theoretical and seeks clarification on its ability to develop an intuitive understanding of tensors.
  • A later reply describes Bishop's book as rigorous with few diagrams but clear, noting that it includes applications to mechanics in the final chapter.

Areas of Agreement / Disagreement

Participants do not reach a consensus on a single recommended book, as various titles are suggested, each with differing focuses and levels of theoretical content. The discussion reflects a range of opinions on the suitability of the recommended texts for the intended audience.

Contextual Notes

Some participants express concerns about the theoretical nature of certain books and their alignment with practical applications, indicating a need for clarity on the balance between theory and application in the recommended texts.

bda23
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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.
 
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?
 
Last edited by a moderator:
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.
 

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