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positive definit matrices

  • To: mathgroup at smc.vnet.net
  • Subject: [mg38256] positive definit matrices
  • From: "David R. Hardoon" <davidh at nospam.cs.rhul.ac.uk>
  • Date: Tue, 10 Dec 2002 04:10:27 -0500 (EST)
  • Sender: owner-wri-mathgroup at wolfram.com

Hello,

Can you help me with this small problem.
i need to problem that K-GG' equals a positive definite matrix.
where K is a symmetric positive definite matrix and GG' are its
incomplete cholesky decomposition of it.

going by x'Ax
= x'(K-GG')x
= x'Kx - x'GG'x

now I know I need to use induction here, but I am unsure how...

in the overall proof I want to show that 
||K-GG'|| <= sum(diag(K-GG'))

thank in advance,
David.


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