I am doing an analysis of a theoretical spectroscopy calculation. I take an eigenvector (nx1) and dot it with many zero-order dipole vectors (nx3) to get the dipole contribution to my new eigenstate. Then, the "Intensity" in the spectrum is calculated by taking the mixed dipole vector and taking the magnitude squared. I would like to calculate the contribution of a particular zero-order state to the overall intensity. This gets hairy because of "sum of squares =/= squares of sums".
To more explicitly write out my procedure:
Dot eigenvector with dipole (nx1 . nx3 = nx3)
Take magnitude squared of each dipole vector (|1x3|^2), n times
Get out % contribution of zero order state (one element in nx1 eigenvector) in each eigenvector.