# The tutor shows an example of a projection from one dimension into another.

Let’s imagine we have the vector **v**

3

2

0

which we want to project in the direction of **w**

3

-1

0

The projection matrix, P_{w}, is given by **ww ^{T}**/

**w**:

^{T}wNow, the projection of **v** onto **w**, P_{w}**v**, is

Note that P^{2}_{w}**v** = P_{w}**v**:

Note, also, that P_{w}**v** has the same proportions as **w**.

Source:

Jack of Oracle Tutoring by Jack and Diane, Cambpell River, BC.