I have a data set and I can compute the vector of the principal axis. However i do not know if there is an equation to compute the length of the first principal axis. I know that it related to the largest eigenvalue. But what is exactly the equation?
For now, I just compute very expensively by projecting all data points to the principal axis and compute the maximum distance between every pair of projected points. However it is not efficient.
I tried to find the equation in books but could not find it.