To elaborate, vector v can be represented in basis vectors, with coordinates :

Often, for example in Euclidean space, a vector can be represented graphically with an arrow that has a tail and a head.

Similarly, a three-dimensional vector can be represented by a one-dimensional array of size three.

A vector, which represents a state of the system, in the Hilbert space of square integrable functions is represented by .

The vectors a and b can be represented by complex numbers.

Signed vectors are represented in two's complement form.

A vector can be represented as a 1-dimensional array and is a 1st-order tensor.

The vector is represented by a boldface symbol:

The matrix and the vector can be represented with respect to a right-handed or left-handed coordinate system.

A two-dimensional polar vector v can be represented as any of the following, using either ordered pair or matrix notation: