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: Positive Definite Matrices

  1. Dec 8, 2013 #1
    1. The problem statement, all variables and given/known data


    2. The attempt at a solution

    So part a. makes sense to me, it basically comes down to

    A1 =
    1 -1 -1
    -1 1 1
    -1 1 1

    A2 =
    1 -1 -1
    -1 2 -2
    -1 -2 11

    I'm not sure how to approach part b. because the question doesn't make much sense to me. It's asking to show that f1 is a single perfect square, so my guess is that from A1 I have to derive an expression for f1 that is a single perfect square.

    Haven't really looked to hard at part c, yet.
  2. jcsd
  3. Dec 8, 2013 #2

    Ray Vickson

    User Avatar
    Science Advisor
    Homework Helper

    Use Chpolesky factorization, which works for any positive-semidefinite matrix. (Many discussions assume positive definiteness, but if you go through the material carefully you can show that it applies as well to the semidefinite case.) See, eg., http://en.wikipedia.org/wiki/Cholesky_decomposition .
    In fact, using the Cholesky algorithm is by far the easiest way to test positive definitness or semidefinitness---much easier than dealing with determinants, for example.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted