Principal Axis Theorem

The principal axis theorem is a result in geometry and linear algebra concerning the principal axes of an ellipsoid or hyperboloid, the lines generalizing the major and minor axes of an ellipse or hyperbola. The theorem states that these principal axes are perpendicular to one another and gives a method for locating them. It generalizes the technique of completing the square from elementary algebra, corresponds in linear algebra and functional analysis to the spectral theorem, and underlies principal component analysis and singular value decomposition in statistics as well as the treatment of angular momentum and birefringence in physics. This description is adapted from Wikipedia contributors under CC BY-SA 4.0; changes were made. https://creativecommons.org/licenses/by-sa/4.0/