A vector space is a collection of mathematical objects called vectors, along with some operations you can do on them. Two operations are defined in a vector space: addition of two vectors and multiplication of a vector with a scalar. These operations can change the size of a vector and the direction it points to. The most important thing to understand is that after you do the addition or multiplication, the result is still in the vector space; you have not changed the vector in a way that makes it not a vector anymore. A vector space is often represented using symbols such as formula_1, formula_2 and formula_3.