This essentially reformulates the problem into a system of linear equations, which can be solved using numerous methods such as Gaussian elimination; in practice advanced methods like the block Lanczos algorithm are used, that take advantage of certain properties of the system.
This reinterprets the problem as a system of linear equations that can be solved using methods such as Gaussian elimination; for practical use, more advanced algorithms like the block Lanczos method are employed to leverage the system's inherent features.