Rank vs Order of Tensors | Tensor Basics

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The discussion clarifies the distinction between the rank and order of a tensor, noting that rank refers to the number of basis vectors associated with the tensor, while order typically indicates the number of indices it has. Confusion arises because different sources use these terms interchangeably, leading to misunderstandings. The term "rank of a matrix" is also mentioned, which pertains to the dimension of its range, highlighting the varied meanings of "rank" in different contexts. The dyadic product's classification as a rank one tensor is debated, with references to differing interpretations in literature. Understanding these definitions is crucial for accurate tensor analysis.
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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
 
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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.
 

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