# Math Help - Orthogonal projection.

1. ## 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.

2. ## Re: Orthogonal projection.

How the inner product is defined?

3. ## Re: Orthogonal projection.

The inner product is defined as

<AB> = tr(A'B)

sorry for not including that.

4. ## Re: Orthogonal projection.

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 $\mathbb{R}^{2\times 2}$ the inner product is the usual one in $\mathbb{R}^4$ i.e. $<(x_1,x_2,x_3,x_4),(y_1,y_2,y_3,y_4)>=x_1y_1+x_2y_ 2+x_3y_3+x_4y_4$ . Now, use any of the well known standard methods.