It's easy to find "intuitive" examples of $(0, r)$ tensors or even $(k, r)$ tensors $( k, r > 0)$. For the purposes of this question, I am considering a tensor in the "classical" sense as being represented by a multilinear form. For instance, every inner product space has an associated inner product which is just a $(0, 2)$-tensor that satisfies certain properties. Also, if $V$ is a vector space over a field $\mathbb{F}$ and $V^{*}$ denotes its dual, then the evaluation map $E:V^{*} \times V \rightarrow \mathbb{F}$ given by $E(f,v) = f(v)$ is an example of a $(1, 1)$ tensor. What are some elementary/intuitive examples of $(k,0)$ tensors?
Intuitive Examples of (r,0) Tensors
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