Computing angle of ellipse or ellipsoid

Question

i need you help in solving the following problem:

given the "center form" of ellipsoid:

• A : matrix of d*d where d is the dimension
• c : center of the ellipsoid hold in a vector

how can i compute the tilt/angle of the ellipsoid from these two inputs in Matlab?

Thanks in advance.

Answer 1

Find the eigenvectors of $A$: they define the principal axes of the ellipsoid. From those you can compute any angles of those axes you care to.

You can find a detailed description on p.10ff of the document "Algorithms for Ellipsoids" by Stephen Pope (PDF download).

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