# Is there a way to perform 2-D image rotation by matrix multiplication?

In my understanding, unlike shifting and scaling, image rotation actually rotates the coordinates whereby interpolating the pixels at discrete positions. It is like a projection that discrete values are projected to another plane which are along with the pixel value.

Thus, I am wondering whether we could do 2-D image rotation in a matrix multiplication way which directly perform rotation on the pixel matrix of the image?

Any help is appreciated in advance.

Let's say you have an $M \times N$ image.
If you turn it into a vector in ${R}^{\left( M N \right)}$ and create a matrix which is $\left(M N \right) \times \left( M N \right)$ by multiplication and rearranging the vector from the multiplication result you can reposition any pixels where ever you want.