Yes.

Points can be represented with column matrices.
To do this,
you first need to decide on a **coordinate frame**
(sometimes called just *frame*.
A coordinate frame in consists of a distinguished point
P_{0} (called the origin) and an axis for
each dimension
(often called X and Y).
In 2D space there are two axes; in 3D space
there are three axes
(often called X, Y, and Z).

For now,
let us talk about 2D space.
The left diagram shows a (rather simple)
virtual world in 2D space.
The points and vectors exist in the space
independent of any coordinate frame.
The next diagram shows the **same** virtual
world, this time with
a coordinate frame consisting of
a particular point P_{0}
and two axes.
In this coordinate frame,
the point A is represented by the
column matrix (2, 2)^{T}.

The right diagram shows the **same** virtual world,
but with a different coordinate frame.
In the second coordinate frame,
the point A is represented by the
column matrix (2, 3)^{T}.