Linear algebra: projecting a vector along another one, matrix method.

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, Pw, is given by wwT/wTw:

Now, the projection of v onto w, Pwv, is

Note that P2wv = Pwv:

Note, also, that Pwv has the same proportions as w.

Source:

mit.edu

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

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