For a none trivial solution (i.e. a solution for which not all of are zero),
it is necessary that the determinant of
and in that case there will be an infinite number of solutions.
Let , say, ( arbitrary) and solve for for in terms of
While trying to simplify a solution I came up with the following sparse matrix but don't know how to solve it.
I need to find solutions for satisfying
I would really appreciate if you would point me in finding out
1. Whether there is actually an analytic solution for this
2. If not a suitable numerical technique to find solutions