Linear Algebra, Python, Matrix Factorization, Numpy.
write: (UΣVᵀ)ᵀ( UΣVᵀ) = V Σᵀ Σ Vᵀ. The singular values are the square roots of the eigenvalues of AᵀA. So we’re left with the problem of finding the eigenvalues and eigenvectors of AᵀA: factorize the characteristic polynomial det(AᵀA — λI), and then find the eigenvector of each root by solving (AᵀA