Thread: Orthogonal projection.

Hi.

I am quite clueless about the following problem and need help on where to start.

given

y =

[1 2]
[3 4]

x1 =

[1,0]
[0,0]

x2 =

[1,0]
[0,1]

(these are all 2x2 matricies by the way, not vectors).

Record the orthogonal decomposition of Y obtained by orthogonally projecting Y onto L(X1,X2).


I have no idea where to start on this.

How the inner product is defined?

The inner product is defined as

<AB> = tr(A'B)

sorry for not including that.

Originally Posted by Kuma

The inner product is defined as <AB> = tr(A'B)

Hint Working in coordinates with respect to the canonical basis of the inner product is the usual one in i.e. . Now, use any of the well known standard methods.