Find a matrix P such that P^* MP = I and P^* KP is diagonal.
M =
52 -36
-36 73
K=
108 -94
-94 267
Ok, here's what I get so far.
e-vectors of M:
-4/5
-3/5
and
3/5
-4/5
Which happen to be unit vectors.
So, if I let A =
-4/5 3/5
-3/5 -4/5
then,
A^-1MA =
25 0
0 100
Then, I let B =
1/5 0
0 /10
So, (B^T)(A^T)M(A)(B) = I, so I'm good there.
Does this mean that P = AB?
If I try P^T K BA, I don't get a diagonal in my calculator.
I do not know how to proceed from here.
Thanks.
M =
52 -36
-36 73
K=
108 -94
-94 267
Ok, here's what I get so far.
e-vectors of M:
-4/5
-3/5
and
3/5
-4/5
Which happen to be unit vectors.
So, if I let A =
-4/5 3/5
-3/5 -4/5
then,
A^-1MA =
25 0
0 100
Then, I let B =
1/5 0
0 /10
So, (B^T)(A^T)M(A)(B) = I, so I'm good there.
Does this mean that P = AB?
If I try P^T K BA, I don't get a diagonal in my calculator.
I do not know how to proceed from here.
Thanks.