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(associative property of Matrices), But remember, 𝐴⊺𝐴 is a positive definite matrix. ⟹ 𝑥⃗⊺(𝐴⊺𝐴)𝑥⃗ = 1 represents an ellipsoid with the eigenvectors of 𝐴⊺𝐴 along the principal axes. So the direction of minimum stretching will be along the eigenvector of 𝐴⊺𝐴 with the smallest eigenvalue. Hence, |𝐴𝑥⃗|