MATLAB: A*A’=C

matrixsolution

Hi all,
I need help.
I have A*A' = C, where
 C = [2/3 -1/3 -1/3;-1/3 2/3 -1/3;-1/3 -1/3 2/3]
and A is matrix 3×2.
How to generate A?
Thank You

Best Answer

One solution can be found by using SVD
>> C = [2/3 -1/3 -1/3;-1/3 2/3 -1/3;-1/3 -1/3 2/3]
C =
    0.6667   -0.3333   -0.3333
   -0.3333    0.6667   -0.3333
   -0.3333   -0.3333    0.6667
>> rank(C) % check if C can be factorized with 3x2 matrix
ans =
     2
>> [U,S,V]=svd(C);
>> A = U(:,1:2)*S(1:2,1:2)
A =
   -0.8165    0.0000
    0.4082   -0.7071
    0.4082    0.7071
>> A*A'
ans =
    0.6667   -0.3333   -0.3333
   -0.3333    0.6667   -0.3333
   -0.3333   -0.3333    0.6667
The solution is not uique since you can multiply on the right side of A by any Hermitian matrix of size 2 x 2
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