[R] Positive Definite Matrix

[Mike Marchywka]

>Date: Tue, 1 Feb 2011 15:41:01 +0000
>From: alex.smit4 at gmail.com
>To: spencer.graves at structuremonitoring.com
>CC: r-help at r-project.org; maechler at stat.math.ethz.ch
>Subject: Re: [R] Positive Definite Matrix


>Hello thank you for so much input. I am afraid that I am fairly new to this
and some of the material is above my understanding for the time being and I
am not looking at anything very complex as you will see from the program I
will include.
I have been talking to a fellow colleague I am working with and have come
down to this.
Your input has been invaluable to me learning more about R thank you!
1.As an example, I do not wish to find a near pd matrix but I want to test
wether it is pd or not so I know if I want it or not,as you will see on the
program I want two outputs depending on if it is a pd and symmetric. So I
have written this for one symmetric matrix and it works and one for a non
symmetric one slightly changed but it doesnt work,if you could point out why
this is going wrong that would be helpful. It cant compare the complex
eigenvalues.
[...]

>2. My colleague said why dont we use the Sylvester's Criterion and test the
leading minors. Would something like that work?


This thread seems to have dragged on for a while, what are you trying to do? 
Presumably this is something other than an exercize in R. 
What interpretation do you have for your eignenvalue spectrum or matrix element
? Problems here could point to various features or pathologies or
opportunities at various points in the analysis.