Mathematically, the principal axis theorem is a generalization of the method of completing the square from elementary algebra.
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In linear algebra and functional analysis, the principal axis theorem is a geometrical counterpart of the spectral theorem.
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By the principal axis theorem, the two eigenvectors of the matrix of the quadratic form of a central conic section ( ellipse or hyperbola ) are perpendicular ( major or minor axis of the conic.
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There are two parts to it : one under the assumption that one endpoint of the diameter is on the intersection of the hyperplane H and ( the solid ellipsoid ) E and the other is on the boundary of E ( lying on the E1 side ), and the other where both endpoints lie on the boundary of E ( in which case, the diameter is a diameter of the original ellipsoid, which can be found by the principal axis theorem ) . talk ) 13 : 44, 21 August 2016 ( UTC)
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