The singular value decomposition (SVD) is a very useful technique for dealing with general dense matrix problems. Recent years, SVD has become a computationally viable tool for solving a wide variety of problems raised in many practical applications, such as least-squares data fitting, image compression, facial recognition, principal component analysis, latent semantic analysis, and computing the 2-norm, condition number, and numerical rank of a matrix.
For more information, please refer to SVD.