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Is the ellipsoid's equation in n-dimension looks like this? https://en.wikipedia.org/wiki/Ellipsoid#Standard_equation

Like $x_1^2/r_1^2 + x_2^2/r_2^2 + ... + x_n^2/r_n^2 = 1$

user128576
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    Just like with $2$-dimensional ellypses, there is some orthogonal basis where the equation looks like that (provided the ellipsoid is centered in the origin). –  Aug 07 '19 at 16:50
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    yes, the center is the origin, otherwise you would subtract c1 from x1, c2 from x2 ... if I'm right – user128576 Aug 07 '19 at 16:53

1 Answers1

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In general, the equation of the ellipsoid in $n-$dimensions is: $\sum_{i=1}^{n}\frac{(x_i-p_i)^2}{a_{i}^2}=1$, where the centre have coordinates $P(p_1,p_2,\cdots ,p_n)$, $a_1,a_2,\cdots,a_n$ are the lenght of the semi-axis and $x_1,x_2,\cdots,x_n$ are the $n$ dimensions. I hope it has helped you.

Matteo
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