Sympy-exact witness of the SVD/Frobenius identity on a rank-1 matrix. X = [[3], [4]] has XᵀX = [25], so σ₁ = √25 = 5 exactly — the classical 3-4-5 Pythagorean triple emerging as the top singular value. Simultaneously the Frobenius norm…
Sympy-exact witness of the SVD/Frobenius identity on a rank-1 matrix. X = [[3], [4]] has XᵀX = [25], so σ₁ = √25 = 5 exactly — the classical 3-4-5 Pythagorean triple emerging as the top singular value. Simultaneously the Frobenius norm…