Krylov subspace

Krylov subspace is like a very special playground. All the kids in this playground like to do math problems. These problems are like puzzles and each puzzle has many pieces that all fit together to make a big picture. Kids take the pieces from the puzzles and figure out how to fit them all together. In doing so, they create individual pictures that make up the big picture. It is like a game of putting together a big jigsaw puzzle. Krylov subspace helps the kids figure out the best way to put the pieces together.