Here is an study problem for my final exam tomorrow:
a) Find an orthonormal basis for R3 that includes a vector parallel to
(0, 3, 4)Transpose.
b) Find the representation of (3, 0, 4) with respect to your basis from a).
c) Verify Plancherel's formula for this vector using this representation.
I am pretty sure I can do part c), but I want to make sure I get everything correct up to that point. Any help is much appreciated. Thanks in advance!
I did that because you only gave me one vector so I assumed I could pick the other two at random.
To find a vector parallel, I just visualized the vector and shifted it over.
ok i understand a) now. how about part b) "the representation of (3, 0, 4) with respect to my basis from a)"
...if you try the problem, could you include the answer in your post? I figure if I know the solution I can figure out the problem eventually by trial and error. Without the solutions i just cant tell if correct or not, and dont know when to stop.
Again, thanks for all your help.
that is the basis for R3 parallel to (0, 3, 4). It is not orthonormal yet until I orthonormalize it which I understand how to do. dwSmith, I'm not up to representations yet, and I figured I would post my questions while people are still awake, but I'm going to go back and work on it and post what I get. Again thank you so much.
ok so i performed grahm-schmidt on the parallel basis for r3.
my orthogonal family came out to y1=(1,0,0) y2=(0,1,0) and y3=(0,0,4)
i then orthonormalized them and got z1=(1,0,0) z2=(0,1,0) and z3=(0,0,1)
... i feel like my answer isn't complicated enough...
anyways, then i said that the representation of (3,0,4) with respect to my orthonormalized basis would be Rz = 3z1 + 4z3.
am i on the right track?