Linear Algebra, Python, Matrix Factorization, Numpy.
equation above, we can see that AV = U Σ, which means that for each column vᵢ of V, we have Avᵢ = σᵢuᵢ. A is possibly a non-square matrix, so it can’t have eigenvectors that map a subspace of V onto itself, since the result Avᵢ is in different dimensions. Instead, we get another vector, u in Rᵐ,