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MathGroup Archive 2005

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Re: Quadratic Form Contours

  • To: mathgroup at smc.vnet.net
  • Subject: [mg57732] Re: Quadratic Form Contours
  • From: dh <dh at metrohm.ch>
  • Date: Tue, 7 Jun 2005 02:03:33 -0400 (EDT)
  • References: <d7pa71$sqt$1@smc.vnet.net>
  • Sender: owner-wri-mathgroup at wolfram.com

Hi Joerg,
To use "Ellipsoid" we need the semi-length and directions of the axes.
The direction we obtain from: Eigenvectors[A]
the half-length from: Sqrt[ b/Eigenvalues[A]]
Therefore, an ellipsoid would be specified by:

Ellipsoid[{x,y}, Sqrt[ b/Eigenvalues[A]], Eigenvectors[A] ]

The erason for this is:
If you turn the coordinate system in direction of the Eigenvectors, the 
quadratic form looks like:

x1^2/ew1 + x2^2/ew2 == b

where ew means eigenvalue.
sincerely, Daniel

Joerg Schaber wrote:
> Hi,
> 
> does anybody know a simple way to calculate 2-D ellipsoids in x={x1,x2} 
> of a quadatric form solving xAx=b for a graphical output, i.e. contour 
> lines of the quadrtic form expressed as the Graphics primitive Ellipsoid?
> I suppose that the option ParameterConfidenceRegion of NonlinearRegress 
> does something like that, but how?
> 
> best,
> 
> joerg
> 


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