ELI5: Explain Like I'm 5

vector spaces and transformations

Vector spaces and transformations are like kids playing with blocks. In this game, each block is like an arrow or vector. Transforming the blocks, also known as vectors, means you change their length and direction. So, if you have a long block and you make it shorter, or if you turn it to a different direction, you are transforming the block. Vector spaces are the sets of blocks that you work with. For example, if you have a set of ten blocks, then your vector space is the set of ten blocks. You can then transform or move these blocks in different ways.