Basis vectors

There are a few special unit vectors used in vector calculus and in linear algebra, which are called the standard basis vectors.

In two-dimensional space, we define two specific basis vectors, and . Based on their components, we can see that they have both length of .

In three-dimensional space, the basis vectors are , , and .

Sometimes the basis vectors can be represented without the hat, just as the bolded characters i, j and k.