1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: Linear Algebra problem (Least Squares?)

  1. Jun 28, 2012 #1
    Linear Algebra problem (Least Squares? - Distance between lines)

    1. The problem statement, all variables and given/known data

    We have two points R = (x,x,x) and S = (y,3y,-1). All we know is that they are on lines somewhere in 3-space and that they don't cross. Need to find an x and y that minimize || R - S ||2

    2. Relevant equations

    ATAx = ATb

    3. The attempt at a solution

    I tried using the equation above, i.e. inverting (ATA) and multiplying both sides with that, but the resulting matrix that I got was a 2x1 matrix of zeros. This is definitely not the right answer. I also tried using (C+D(t)-b)2... for each coord and doing a partial derivative for C and D, but I ended up getting the same equation for both derivatives, which I am sure is not right.

    I am very confused and not sure where to go from here.
    Last edited: Jun 28, 2012
  2. jcsd
  3. Jun 29, 2012 #2
    Why don't you minimize it in the usual way, [tex] \nabla ||R-S||^2 = 0 [/tex] ?
  4. Jun 29, 2012 #3
    That is what I tried. At least that's what I think I tried. That was where the (C+D(t)-b)2... etc, was about in my previous post. (C+Dx - y)2 + (C+Dx - 3y)2 + (C+Dx + 1)2.

    But, since the t (x) values are all x's, they cancel with the two's after I do the partial derivative w/respect to D, and both derivatives end up the same. Is there something I'm missing, or am I doing something wrong?
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook