Rank vs Order of Tensors | Tensor Basics

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The discussion clarifies the distinction between the rank and order of tensors, as outlined in "Mathematical Physics 2nd Ed" by Kusse and Westwig. The rank of a tensor is defined as the number of basis vectors it possesses, while the term "order" is often used interchangeably in some texts, leading to confusion. It is important to note that the rank of a matrix refers to the dimension of its range, which differs from the tensor rank. The dyadic product between vectors results in a tensor of rank one, aligning with the definitions provided in the referenced literature.

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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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