Block LU decomposition

A block LU decomposition is a way to break a matrix (which is like a larger grid made up of smaller grids or blocks inside it) into smaller parts. We can then use these smaller blocks to help us solve problems with the matrix. To do this, we start by putting a line across it to break it into two pieces, then we put another line down and break it into four pieces. This process keeps going until we get many small blocks. Each block can then be solved on its own, which makes it easier to solve big problems with the whole matrix.