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that 𝑦⊺Λ𝑦 = 1 looks like the equation for an ellipsoid. We can rewrite this equation as: This equation definitely represents an ellipsoid where 1/√𝜆1, 1/√𝜆2, … 1/√𝜆𝑛 are half the lengths of the principal axes. Back to our example, 𝐴 = [[5,4],[4,5]], and the eigenvalues of 𝐴 are 1 and 9.