Learning tensors for evolutionary or developmental biology

Question

I'm looking for book recommendations on tensor algebra for use in biology.

Tensors are being used increasingly in evolutionary biology and developmental biology, it seems. For example, here is an example of an empirical study that makes use of tensors in its analysis of data: http://rspb.royalsocietypublishing.org/content/282/1819/20151119

There are lots of books on the mathematics of tensors, and many introductions online. So far, what I have found is that either (a) the presentation is heavily oriented toward physics applications, or (b) the presentation begins from an abstract algebra (or category theory?) point of view.

I'm willing to work through physics-style or abstract algebra presentations of tensor concepts and methods, but I am wondering whether there are any textbooks or other introductions that someone would recommend for biological applications.

(I have read the brief appendix on tensors in Sean Rice's book Evolutionary Theory. Although I've found his other mathematical appendices and most of the mathematics in the book accessible, the tensor material in the book is too brief for me--I need more.)

Answer 1

The field of tensor decompositons has been discovered in many fields simultaneously, each with their own notation. Many modern notation in fields like CS or STAT have originated from the work of Tamara Kolda http://www.kolda.net/publication/koba09/ However, this is restricted to the CP and Tucker decomposition, and we have many others now. See https://arxiv.org/pdf/1609.00893.pdf and https://arxiv.org/abs/1708.09165