Machine Learning, Artificial Intelligence, Mathematics.
orthonormal eigenvectors of AᵀA, we can calculate the value of uᵢᵀuⱼ as It equals zero. i.e. uᵢ and uⱼ are orthogonal with each other. As shown previously, they are also eigenvectors of AAᵀ. From Avᵢ = σuᵢ, we can recognize that uᵢ is a column vector of A. Because A has a rank of r, we can choose