Two-point Tensor - The Most Mundane Example of A Two-point Tensor

The Most Mundane Example of A Two-point Tensor

The most mundane example of a two-point tensor is the transformation tensor, the Q in the above discussion. Note that

.

Now, writing out in full,

and also

.

This then requires Q to be of the form

.

By definition of tensor product,

So we can write

Thus

Incorporating (1), we have

.