Given a matrix with components
where a is a constant real vector, find the eigenvalues of the matrix.
I can't really see where to start with this - any hints to see the obvious that I may have missed?
The formula uses the Kronecker delta:
That is a short way of writing
But it doesn't make a whole lot of sense.
I would recommend looking at "easy" cases to start with (always a good strategy).
For n= 1, this operator is just "1+ a" and its operation is just multiplying the number x: for , of course.
For n= 2, this operator can be represented by the matrix . What are its eigenvalues?
For n= 3, this operator can be represented by the matrix .
What are its eigenvalues?