Let A

If \(\displaystyle (A \cdot B) \) = \(\displaystyle A^* \cdot B^* \) and \(\displaystyle (A^*)^* = A \) ,

Then \(\displaystyle (A^* \cdot A)^* \) = \(\displaystyle (A^*)^* \cdot A^* \) = \(\displaystyle A \cdot A^* \)

But then also

\(\displaystyle (A^* \cdot A)^* = \overline{(\overline{A^\top}\cdot A)^\top} = (A^* \cdot A) \)

What am I doing wrong?

EDIT: Also, where can I find a comprehensive guide for the forum notations?

Thanks

_{m,n}be any matrixIf \(\displaystyle (A \cdot B) \) = \(\displaystyle A^* \cdot B^* \) and \(\displaystyle (A^*)^* = A \) ,

Then \(\displaystyle (A^* \cdot A)^* \) = \(\displaystyle (A^*)^* \cdot A^* \) = \(\displaystyle A \cdot A^* \)

But then also

\(\displaystyle (A^* \cdot A)^* = \overline{(\overline{A^\top}\cdot A)^\top} = (A^* \cdot A) \)

What am I doing wrong?

EDIT: Also, where can I find a comprehensive guide for the forum notations?

Thanks

Last edited: