# Reverse matrix operation that makes it symmetric.

given a symmetric matrix $A = \frac{B+B^T}{2}$ can i retrieve B? Or has that information been lost...

• No: you can't. Information is lost. – Crostul Apr 24 '17 at 17:15
• Adding any two anti symmetric matrices will result in zero. – copper.hat Apr 24 '17 at 17:15
• “I'm thinking of two numbers whose average is 6. What are they?” Can you see how that's the same question? – Matthew Leingang Apr 24 '17 at 17:17
• @MatthewLeingang Yes, but i thought since it was B twise... there was something there. – Evan Apr 24 '17 at 17:21
• You're part right, as @OpenBall points out. – Matthew Leingang Apr 24 '17 at 17:26

You can retrieve the diagonal elements of $B$, but not all of $B$. Consider:
$$B = \begin{bmatrix} 1 & 2 \\ 2 & 1 \end{bmatrix}$$
$$B = \begin{bmatrix} 1 & 3 \\ 1 & 1 \end{bmatrix}$$