# Deriving X from X'X

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Colette Salemi on 2 Oct 2016
Commented: Colette Salemi on 6 Oct 2016
Hello, I am hoping someone can help me determine the n x k matrix X when the k x k matrix X'X is given using Matlab. Please share any coding tips! Many thanks!!
Walter Roberson on 2 Oct 2016
if n > k then there will cannot be a unique solution, as k x k would not have enough information to find n x k when n > k.
If n < k then round-off error has the potential to be a problem.
Colette Salemi on 6 Oct 2016
Thank you! I was working on a problem set where we were provided with X'X, and my first instinct was to try to derive X. As you point out this isn't possible with the information given (instead we used the info in X'X). Thanks again for your help!

Jang geun Choi on 2 Oct 2016
Edited: Jang geun Choi on 2 Oct 2016
n=2;
k=3;
X=rand(n,k); % make sample matrix X
Xn=X'*X
Is it right what you want?

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