On Oct 30, 11:07 pm, MBALOVER <mbalov...@gmail.com> wrote: > Hi all, > > 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. > > Could you please help? > > Thank you.
The first eigenvalue is the sum of squares of the projections of the points onto the first principal axis. If by "length" you mean the difference between the maximum and minimum projections onto the axis then the eigenvalue only bounds the length; to get the actual length you need to find the maximum and minimum projections.