Books/resources for exercises on tensors and multilinear algebra

[Shirish]

I'm self-studying tensors from a book that doesn't have exercises. The book is Semi-Riemannian Geometry by Newman. To get a better feel for index manipulation, tensor results and calculations, I'm looking for a book that has many exercises in these topics.

I'd be grateful if those knowledgeable in the subject can point me to such books. The end use case is to get comfortable enough with tensor and index machinery that I can easily do calculations in Physics (e.g. special/general relativity, etc.)

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I've studied till chapter 6, ToC here : https://onlinelibrary.wiley.com/doi/book/10.1002/9781119517566

More specifically, the topics I've covered so far are: vectors, covectors, basic linalg results, linear transformations, matrix representations of transformations/vectors/covectors, change of basis, tensors, basis/components of tensor spaces, sums/direct sums, subspace annihilator, pullback of covectors/covariant tensors by a linear transformation, ordinary and metric contraction of tensors, bilinear functions, inner product space, adjoints, orthonormal bases, linear isometries, perp, time cones, Lorentz vector spaces, flat/sharp maps and index raising/lowering (for vectors/covectors only so far).

 

[jedishrfu]

Schaums Outlines has a text on Tensor Analysis with lots of problems:

https://www.amazon.com/dp/0071756035/?tag=pfamazon01-20

 

[WWGD]

I think Schaum's is underrated.

 

[jedishrfu]

My issue with Schaum's is that while good, the books never covered exactly what my course covered. I attributed it to the books being written a few years earlier and that my prof was somewhat eccentric in the topics chosen. I recall trying to learn Lagrangian physics from them for a course using Marion's book and finding the problems didn't match at all what we were doing.

In contrast, they worked great for self-study. I learned Calculus, Vector, and Tensor Calculus that way before taking the courses.

 

[WWGD]

My issue with Schaum's is that while good, the books never covered exactly what my course covered. I attributed it to the books being written a few years earlier and that my prof was somewhat eccentric in the topics chosen. I recall trying to learn Lagrangian physics from them for a course using Marion's book and finding the problems didn't match at all what we were doing.

In contrast, they worked great for self-study. I learned Calculus, Vector, and Tensor Calculus that way before taking the courses.

I think they're good as a complement , for independent study and/or as a prep for the class.

 

[George Jones]

I'm self-studying tensors from a book that doesn't have exercises. The book is Semi-Riemannian Geometry by Newman. To get a better feel for index manipulation, tensor results and calculations, I'm looking for a book that has many exercises in these topics.

I'd be grateful if those knowledgeable in the subject can point me to such books. The end use case is to get comfortable enough with tensor and index machinery that I can easily do calculations in Physics (e.g. special/general relativity, etc.)

A nice complement to the book your studying is the book "A General Relativity Workbook" by Thomas Moore. There is nary a (coordinate-free) multilinear map to be seen, but there is nice coverage of "index gymnastics".

I personally find that coordinates and indices can be useful for calculation, and that coordinate-free notation often is useful conceptually, although these aren't completely general statements.

 

[Shirish]

A nice complement to the book your studying is the book "A General Relativity Workbook" by Thomas Moore. There is nary a (coordinate-free) multilinear map to be seen, but there is nice coverage of "index gymnastics".

I personally find that coordinates and indices can be useful for calculation, and that coordinate-free notation often is useful conceptually, although these aren't completely general statements.

I had a look at this book - it seems nice! I'll update more in this thread as and when I find more resources with exercises.