I am trying to understand Singular Value Decomposition from a intuitive point of view. As we know by applying SVD to any matrix, we get these three matrices as U, Sigma, V. And a matrix multiplication can be interpreted as a combination of rotation and scaling. Here U & V corresponds to the rotation performed by that matrix and Sigma the scaling factor.

My question is, why do we get or need two rotation matrices or unitary matrices (U & V), instead of one?