Matrix decomposition methods are a foundation of linear algebra in computers, even for basic operations such as solving systems of linear equations, calculating the inverse, and calculating the determinant of a matrix. Enormous data sets carry with them enormous challenges in data processing. Solving a system of 10 equations in 10 unknowns is easy, and one need not be terribly careful about methodology. But as the size of the system grows, algorithmic complexity and efficiency become critical. Matrix decompositions are an important step in solving linear systems in a computationally efficient manner. This book provides a complete overview of the concepts, theories, algorithms, and applications related to robust low-rank and sparse matrix decompositions