Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Matrix form - completing the square

  1. Jul 29, 2011 #1

    if B is a positive semi definite matrix, how can you complete the square around B from

    x'Bx + x'Cy + y'C'x, where C is also a matrix.

    The answer is (x+B^-1Cy)'B(x+B^-1Cy) + y'C'B^-1Cy

    I have not come across completing the square using matrix notation before - thoughts appreciated.

  2. jcsd
  3. Jul 29, 2011 #2


    User Avatar
    Science Advisor
    Homework Helper

    Hello Emma! :smile:

    (try using the X2 icon just above the Reply box :wink:)

    I don't think I'd call that "completing the square", since it's the sum of two squares.

    But you can easily check it (there seems to be an error :redface:) using (B-1Cy)' = y'C'B-1' :wink:
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook