$A$ is known and diagonal, $C$ is known and symmetric and $B$ is symmetric. All matrices are positive semi-definite and of full rank.
Asked
Active
Viewed 57 times
1 Answers
1
I will assume that $A$ is invertible, since otherwise, the answer is a clear no. Rewrite the equation as $A^{1/2}CA^{1/2}=(A^{1/2}BA^{1/2})^2$, where $A^{1/2}$ is the unique positive definite square root of $A$. But then we must have $A^{1/2}BA^{1/2}=(A^{1/2}CA^{1/2})^{1/2}$, and hence $B=A^{-1/2}(A^{1/2}CA^{1/2})^{1/2}A^{-1/2}$.
Harald Hanche-Olsen
- 31,960
-
If i follow correctly, it means that it is sufficient for A to be positive definite and i don't need it to be diagonal right? @Harald – Yair Yakoby May 11 '17 at 08:28
-
Yes, that is right. – Harald Hanche-Olsen May 11 '17 at 08:32