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: A Schur complement application

  1. Feb 29, 2016 #1
    Hi all,

    I have the following BMI (knowing that P, K and ##\gamma## are unknown with appropriate dimensions; the others are known).
    [ {\begin{array}{*{20}{c}}
    {{A^T}P + {K^T}{B^T}P + PA + PBK + C_z^T{C_z}}&{P{B_w}} \\
    {B_w^TP}&{ - \gamma }
    \end{array}} ] < 0

    I would like to know if the above inequality are equivalent to the following by using Schur Complement:

    [ {\begin{array}{*{20}{c}}
    {{A^T}P + {K^T}{B^T}P + PA + PBK}&{C_z^T}&{P{B_w}} \\
    {{C_z}}&{ - 1}&0 \\
    {B_w^TP}&0&{ - \gamma }
    \end{array}} ] < 0

    3. The attempt at a solution

    Thank you very much in advance for your replies.

    Kind regards,
    Last edited by a moderator: Feb 29, 2016
  2. jcsd
  3. Feb 29, 2016 #2


    Staff: Mentor

    In future posts, please don't delete the homework template. Its use is required.
    What does the above mean?
    You've written it using LaTeX as an array, but an array is not a number, so can't be negative, positive, or even zero.

    Also, what is BMI?
    Same comment here.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted