Are rank and order the same thing for tensors?

[Pollywoggy]

I am confused about the difference between the rank and order of a tensor.

On p 71 of Mathematical Physics 2nd Ed (Kusse and Westwig, 2006 Wiley-VCH), the rank of a tensor is described as identifying the number of basis vectors of the tensor but in some other books, this seems to be described as the order of a tensor.

Online, I saw both terms used as though they refer to different things, but I can't rely on that information because I saw it in Wikipedia. In Wikipedia, I also saw a statement that the dyadic product between vectors creates a tensor of rank one, but that is not what I read in the book mentioned above.


thanks

 

[Dick]

The phrase "rank of a tensor" generally just refers to how many and what type of indices it has. "rank of a matrix" usually means the dimension of it's range. They are two completely different usages of the word "rank". The second meaning is what the wikipedia entry is referring to.