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

A condition on principle minors of a symmetric Positive semidefinite (PSD) matrix

  1. Apr 3, 2010 #1
    Hi everyone,
    Let [tex] A=(a_{ij})[/tex] be a symmetric (i.e., over reals) PSD matrix. Then is the following correct?

    "If any principle minor ( [tex] \ne A [/tex] ) be zero, then all principle minor contained in this minor should also be zero".

    I can not prove or disprove it..any help?

    By the way how the result will change if we consider Hermitian matrix (over complex) instead of symmetric matrix?

    Thanks
     
  2. jcsd
  3. Apr 7, 2010 #2
    Oh..I got the answer. Its not correct. Consider the diagonal matrix: D={1,1,0,1,...}. Clearly $A_33=0$ but $A_22$ is non-zero.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook