let s*s'=R
where s is a vector and s' means Hermitian of s
I have matrix R. but I don't have s . Is there any solution to obtain s from R ?
Dear Houman Parsaei
If your R indeed has the form SST, and the entries are real, then
the components of S are the square roots of the diagonal entries.
Example: If R = [ 4 6
6 9 ]
then ST = [ sqrt(4), sqrt(9) ] = [ 2, 3].
This is true for any dimension of S.
Best regards
Dear Houman Parsaei
If your R indeed has the form SST, and the entries are real, then
the components of S are the square roots of the diagonal entries.
Example: If R = [ 4 6
6 9 ]
then ST = [ sqrt(4), sqrt(9) ] = [ 2, 3].
This is true for any dimension of S.
Best regards
Dear Houman
This kind of matrices is said in elementary algebra the Gram matrix of the vector s. The answers given by colleagues above are fruitful. I'd like to precise that in stochastic and statistic frameworks, there are other methods to estimate s with prescripted behavior of its components.
For instance, if you need just to estmate s without any other constraining hothesis, you may choose as proposed square roots of diagonal coefficients.
Good luck
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