- #1
asif zaidi
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I did some problems from the example and the questions at end of chapter. I got all of them right except this one.
Problem Statement:
Consider the matrix [3 0; 0 -2]. Find its singular value decompositions
Problem Solution
Goal is to find A = U*S*V as below
Step1: Find AA', A'A. In this case they both are equal and are [9 0; 0 4];
Step2: Find U = eig vector (AA'). Doing so gives [1 0; 0 1];
Step 3: Find S = [3 0; 0 2] (I am not showing the steps)
Step 4: Find V = eig vector (A'A). Doing so gives [1 0; 0 1];
Verify: Multiply U*S*V and it should give back A.
My problem is it gives [3 0; 0 2] which is different than A = [3 0; 0 -2].
I know that if I change V to [1 0 ; 0 -1] I will get A back. But why do my computations not show this. What am I missing?
Like I said, I did the above procedure for a lot of other numbers and I get it right. Only when I have a negative value in the matrix then it seems I am missing a -1 factor which I cannot get from my procedure.
Thanks
Asif
Problem Statement:
Consider the matrix [3 0; 0 -2]. Find its singular value decompositions
Problem Solution
Goal is to find A = U*S*V as below
Step1: Find AA', A'A. In this case they both are equal and are [9 0; 0 4];
Step2: Find U = eig vector (AA'). Doing so gives [1 0; 0 1];
Step 3: Find S = [3 0; 0 2] (I am not showing the steps)
Step 4: Find V = eig vector (A'A). Doing so gives [1 0; 0 1];
Verify: Multiply U*S*V and it should give back A.
My problem is it gives [3 0; 0 2] which is different than A = [3 0; 0 -2].
I know that if I change V to [1 0 ; 0 -1] I will get A back. But why do my computations not show this. What am I missing?
Like I said, I did the above procedure for a lot of other numbers and I get it right. Only when I have a negative value in the matrix then it seems I am missing a -1 factor which I cannot get from my procedure.
Thanks
Asif