Two-point Tensor - The Transformation Law For Two-point Tensor

The Transformation Law For Two-point Tensor

Suppose we have two coordinate systems one primed and another unprimed and a vectors' components transform between them as

.

For tensors suppose we then have

.

A tensor in the system . In another system, let the same tensor be given by

.

We can say

.

Then

is the routine tensor transformation. But a two-point tensor between these systems is just

which transforms as

.