I have a matrix A and I need to write it as $A=UU^T$ and also to write the matrix as$A=U^T U$ . I am wondering how I can find U.
decomposition of matrix A as $A=UU^T$
0
$\begingroup$
linear-algebra
-
0For starters, for this to be possible you must have $A^T = A$. Is it the case? – 2017-02-14
-
1https://en.wikipedia.org/wiki/Cholesky_decomposition – 2017-02-14
-
0The Cholesky decomposition will solve either $U^TU = A$ or $UU^T = A$, but in general not both of them. If there is at least one $U$ with $A = UU^T$, then we know that $A$ is positive semidefinite. In this case, there is a symmetric "square root" of $A$, i.e. there is a symmetric matrix $U$ with $U^2 = A$. With this $U$, you have $A = U^2 = UU^T = U^TU$. https://en.wikipedia.org/wiki/Square_root_of_a_matrix – 2017-02-14