Eugene E. answered • 12/29/17

Tutor

New to Wyzant
Let A be a square matrix and let A* denote the adjoint of A. Set A

_{1 }= (A + A*)/2 and A_{2 }= (A - A*)/2. Note A_{1 }+ A_{2 }= A. Since (A*)* = A, then(A

_{1})* = (A* + A)/2 = A_{1 }_{}(A

_{2})* = (A* - A)/2 = -(A - A*)/2 = -A_{2 }Therefore A

_{1 }is Hermitian and A_{2 }is skew-Hermitian.
Log O.

12/29/17