An analytical method is presented for determining if two ellipsoids share the same volume. The formulation involves adding an extra dimension to the solution space and examining eigenvalues that are associated with degenerate quadric surfaces. The eigenvalue behavior is characterized and then demonstrated with an example. The same method is also used to determine if two ellipsoids appear to share the same projected area based on an oberver's viewing angle. The following approach yields direct results without approximation, iteration, or any form of numerical search. It is computationally efficient in the sense that no dimensional distortions, coordinate rotations, transformations, or eigenvector computations are needed.
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