In the tensor product , we defined a “pure tensor” to be an element of the form where .
1. I warned you that not every element in is a pure tensor. Can you give an example of this? (Do keep in mind that something that does not immediately look like a pure tensor, such as , might actually be a pure tensor. In this case it is .)
2. Samantha asked a good question: How can we tell if two pure tensors and are equal to each other? Any thoughts? Is this easy? Is this hard?