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An ellipsoid is a subset of
 consisting of points
 such that $$ \left(\frac{x}{a}\right)^2+ \left(\frac{y}{b}\right)^2+ \left(\frac{z}{c}\right)^2=1 $$ for some $a,b,c>0$ .
- If $a=b=c$ , the ellipsoid reduces to a sphere.
- If we fix the value of any of $x,y,z$ to some constant, say $x=C$ , we obtain an ellipse in the plane $(C,y,z)$ .
- The ellipse determined by $a,b,c$ is the unit sphere of the norm $$ \Vert v \Vert = v^T \operatorname{diag} (\frac{1}{a}, \frac{1}{b}, \frac{1}{c}) v, \quad v=(x,y,z)^T. $$
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"ellipsoid" is owned by matte.
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Cross-references: norm, unit sphere, plane, ellipse, fix, sphere, points, subset
There are 8 references to this entry.
This is version 3 of ellipsoid, born on 2005-01-12, modified 2005-02-19.
Object id is 6637, canonical name is Ellipsoid.
Accessed 4825 times total.
Classification:
| AMS MSC: | 51M05 (Geometry :: Real and complex geometry :: Euclidean geometries and generalizations) |
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Pending Errata and Addenda
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