Education, Artificial Intelligence, Computer Vision.
ellipsoid: consider 𝑥⊺𝐴𝑥 = 𝑥⊺(𝑄Λ𝑄⊺)𝑥 (𝐴 = 𝑄Λ𝑄⊺) = (𝑥⊺𝑄)Λ(𝑄⊺𝑥) (Matrix Multiplication is associative) but, 𝑦 = 𝑄⊺𝑥 and 𝑦⊺ = 𝑥⊺𝑄 substituting y in the equation, we get: 𝑥⊺𝐴𝑥 = 𝑦⊺Λ𝑦 Let’s see how 𝑦⊺Λ𝑦 looks like: Here 𝑦1, 𝑦2, …, 𝑦𝑛 are the components or the coefficients of the vector 𝑦⃗. We can see