SVD takes any m x n matrix A, and then returns three matrices in return—U, Σ, and V. Here, U is an m x m unitary matrix, Σ is an m x n diagonal matrix, and V is an n x n unitary matrix. By unitary, we mean that a matrix's columns form an orthonormal basis; by diagonal, we mean that all values in the matrix are zero, except for possibly the values along its diagonal.
The significance of the SVD is that this decomposes A into these matrices so that we have A = UΣVT ; moreover, the values along the diagonal of Σ will all be positive or zero, and are known as the singular values. We will see some applications of this soon, but you should keep in mind that the computational complexity of SVD is of the order O( ...
