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.