Rabbits Eleven

What if we just watch tensors in the wild to see what they do?

For the next part, we aren’t questioning what the author is doing. Instead, we assume it is correct and they we are asking “what must be true” given what the author did?

The author is putting superscripts and subscripts before the symbol to explain the rank of the symbol.:

_2^0{T}(\overrightarrow u, \overrightarrow v) = \overrightarrow u \cdot \overrightarrow v

When _2^0{T} takes two vectors, it becomes a scalar.

Next we were asked to change the story by holding one vector constant so we would have a function of only one variable. The author chose to hold \overrightarrow v did the following:

_2^0{T}(\overrightarrow u, \overrightarrow v) = \overrightarrow u \cdot \overrightarrow A

\overrightarrow A = \: _1^1{T}(\overrightarrow v)

For everything to remain true, \overrightarrow A must take a vector and make a vector.

So far, from what we’ve seen, each time we feed a vector to a tensor the subscript value decreases by 1.