Quote:Original post by acp693
Thanks, That's what I first thought, however consider the simpler case of
x direction vector= Magnitude 6, phase 0 degrees, (6+0i)
y direction vector= magnitude 6, phase 90 degrees,(0+6i)
Oh, your problem is not the problem I thought you had...
Anyway, here's how I'd think about it. From my last post you see how you can represent a phase-shifted sinusoid either in "polar" (magitude/phase), or "cartesian" (cosine term, sine term) form. Well that means that you can write your point (x,y)(t) as,
[ x(t) ] [ A1 B1 ] [ cos(t) ][ ] = [ ] [ ][ y(t) ] [ A2 B2 ] [ sin(t) ]or more simply, just
p(t) = M u(t)
where u(t) is a unit vector for all time, and p=(x,y).
What unit vector u maximizes the norm of the expression "M u" ? Simply the one corresponding to the largest singular value of M! Equivalently: The eigenvector corresponding to the largest eigenvalue of MT M.
