Just check it is orthogonal and that each row has its norm equal to 1. That won't be very troublesome
How do you, properly, verify that a given matrix is a rotation matrix?
Consider the following matrix P:
where (for ) and else .
It's essentially an identity matrix with that familiar 2x2 rotation matrix setup sort of in the middle there. But mathematically, what conditions must I show are true to establish that this is a rotation matrix? I would think orthogonality is one of them?
Thank you in advance!
(sorry for the missing \cdots, I exceeded the limit of latex code)
I'm sorry to bother you with more of these simple questions, but when verifying , is it ok notation-wise to omit the larger part of and only show calculations on a smaller part containing the cos and sin elements? Then show that they either go to 1 or 0 and thus .
Well that depends on the corrector... So it's hard to answer you!
But even the more detailled version of the answer is not that bad: let's say
If or then for any otherwise it is zero, hence
Now and ... I guess it is evident with the form of theese lines/rows.