2
votes
1answer
25 views

Building intuition for tensors in machine learning

I'm trying to understand tensors in the context of machine learning, but all the resources that mention tensors that I've found so far were building the intuitions through physics applications. As ...
0
votes
0answers
40 views

Divergence of a Tensor Examples?

Would anyone have a reference to a book where explicit examples of things like taking the divergence of a tensor (page 4) are given? Stupid computational examples like the one given here (bottom of ...
2
votes
3answers
240 views

Resources for properly developing a modern understanding tensors

I am currently learning about tensors as they come up in the mathematics behind continuum mechanics. I was fairly disappointed with my initial foray into tensors, as presented in the book Classical ...
7
votes
1answer
494 views

I feel that (physics) notation for tensor calculus is awful. Are there any alternative notations worth looking into?

I am reading through Fung and Tong's "Classical and Computational Solid Mechanics", and feel that the Einstein summation convention saves a few symbols, at the expense of a lot of clarity. Along with ...
2
votes
1answer
133 views

How to translate between differential forms and tensor index notation

The books on Manifold theory & geometry that I studied introduce connection and curvature in the language of differential forms. But Physics books on the other hand like (General Relativity by ...
0
votes
2answers
106 views

Tensors - need materials to study

I want to study about tensors. Can you indicate me some materials, papers, books which I should begin. I tried last year to study but it seems to hard for me. Thanks for help :)
1
vote
0answers
101 views

Rank-2n tensor algebra eigenvalue equation

Im interested in resources and work done on the eigenvalue equation for rank-2n tensors: $$ M_{ij}A_{j} = \lambda A_{i} \\ $$ $$ M_{ijkl}A_{kl} = \lambda A_{ij} \\ $$ $$ M_{ijklmn}A_{lmn} = \lambda ...
10
votes
5answers
456 views

Book on tensors

Can anyone recommend me a book on tensors with an intuitive approach? I have some course notes on that subject, but it's really abstract and theoretical. I want to understand why tensors were ...
1
vote
1answer
278 views

Index notation clarification

Previously, I have seen matrix notation of the form $T_{ij}$ and all the indices have been in the form of subscripts, such that $T_{ij}x_j$ implies contraction over $j$. However, recently I saw ...
6
votes
2answers
162 views

Reference for densities and pseudoforms and non-tensorial representations of $\operatorname{GL}(n)$ and associated vector bundles

I'm looking for a reference that will set me straight on a few things. It started out with densities. In John Lee's book, "Introduction to Smooth Manifolds", densities on vector spaces are functions ...
4
votes
2answers
1k views

Mathematically Precise Definition of Covariant and Contravariant Transformation

I am trying to understand the meanings of "covariant transformation" and "contravariant transformation" and how they are related. I have read the related Wikipedia article and still feel I cannot ...