I'm trying to rotate a $100 \times 50$ matrix, $A$. I understood I should be able to do this with a $50 \times 50$ rotation matrix $B$, and that the other $50$ would still be rotated the correct amount, by dot multiplying $AB$ - so, Q.1. is this correct?
$B$ is a $U$ matrix from SVD as my rotation matrix - as it is orthonormal, with a determinant of $-1$, I assumed I could use this as a rotation matrix - Q.2. is this correct?
I have tried adding $-1$ at the top left corner of each matrix in case it mattered that $B$'s determinant was $-1$ instead of $1$, but it didn't help this problem
$A$, if it were $100 \times 100$, would be a $100 \times 100$ identity matrix with only row $1$ and column $1$ of entries - the row and column are the same. I have put a straight line in there for now. Here is a graph of $A$:
When I rotate by $B$, the line is no longer aligned after row $50$:
e.g. column $1$:
column 2:
etc.
It looks like the line at row $50$ just takes something like the average value of all the others. I would like it to follow the trend of the line prior to this point, instead. Is there a better way of doing this? Is what I'm trying to do impossible?