Though I understand what Tensors are intuitively, I have trouble understanding what spinors are. Similar to how tensors are "things that transform like a tensor", I am not sure if spinors are also "things that transform like a spinor".
I know that spinors, under a $\theta$ rotation with respect to the $\hat{n}$ axis, transform as:
$$\psi' = (I\cos(\frac{\theta}{2})+i(\hat{n}\cdot \vec{\sigma})\sin(\frac{\theta}{2}))\psi$$
and I see how you need to apply the transformation twice in order for the spinor to remain the same.
However, this is just rotation. Given any transformation (and let's say for simplicity a linear transformation of coordinates), how can I find how a spinor would transform?
