(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Let R={[x,y,z,w]:x=y and z=w} and N={[x,y,z,w]:x=-y and z=-w}

Find the rule in standard coordinates for the projection of R4x1 onto R along N

2. Relevant equations

3. The attempt at a solution

I have B wrt R as {[1,1,0,0],[0,0,1,1]} and B wrt N as {[1,-1,0,0], [0,0,1,-1]}, so my basis is {[1,1,0,0],[0,0,1,1],[1,-1,0,0],[0,0,1,-1]}.

[E]B=

[1 0 0 0

0 1 0 0

0 0 0 0

0 0 0 0]

I used my basis as my Q^(-1), so

Q=

[.5 .5 0 0

0 0 .5 .5

.5 -.5 0 0

0 0 .5 -.5]

which gives me

Q^(-1)[E]BQ=

[.5 .5 0 0

.5 .5 0 0

0 0 .5 .5

0 0 .5 .5]

so my rule would be

E[x =

y

z

w]

[x+y

x+y

z+w

z+w]

but,

E[1 =

1

0

0]

[2

2

0

0]

instead of

[1

1

0

0]

but

E[1 =

-1

0

0]

[0

0

0

0]

which is correct

my Q^(-1) can't be right, but i'm not sure how to find another one.

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# Homework Help: Projections along N

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