A*A'=C

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 3x2.

How to generate A?

Thank You

[madhan ravi]

"A is matrix 3x2."

? A is given?

[Imil Imran]

A is not given, I want to find A

[Image Analyst]

Is this your homework? Homework help

[Walter Roberson]

Looks like there are at least 60 solutions once you realize that the solutions are not restricted to real numbers.

Answer 1

[Bruno Luong]

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

[Imil Imran]

Thank you