Lecture on Conjugate of Matrix
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Conjugate of Matrix (\(A^-\)):

\(A= \begin{bmatrix}3+2i&6+i&4\\4-i&7+2i&3-4i\end{bmatrix} \) then , \(A^-= \begin{bmatrix}3-2i&6-i&4\\4+i&7-2i&3+

4i\end{bmatrix} \) 

Properties of conjugate of matrix are:

  1. \(A^-=A
    \)
  2. \((A+B)^-=A^-+B^-\)
  3. \((KA)^-=K^-A^-
    \)
  4. \((AB)^-=A^-B^-\)
  5. If \((A^-)=-A\) // It means matrix contains only imaginary values

Transpose conjugate (\(A^ \Theta
\)
) = (\(A^-\))'

Properties of transpose conjugate:

  1. \((A^ \Theta )^ \Theta
    \)
    = A
  2. (\((A+B )^ \Theta
    \)
    ) = \((A^ \Theta ) +(B
    ^ \Theta )
    \)
  3. \((AB )^ \Theta=B^ \Theta A^ \Theta\)
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