Re: [理工] [線代] Hermitian and symmetric matrix

[s90413k64 (成言追口河與草)]

: 題目:   [99成大數學]
:         State the defintion of Hermitian matrix.
:         Let A and B be real matrices.
:         If A+iB is a Hermitian matrix,
:         show that [ A -B ] is a symmetric matrix.
:                     B  A


A+iB is a Hermitian

         H
=> (A+iB)  = A+iB


      H    T   T
(A+iB)  = A -iB  = A+iB

因為A and B be real matrices

 T         T
A  = A    B  = -B

             T      T   T
因此 [ A -B ]  = [ A   B ] = [ A -B ]
       B  A          T  T      B  A
                 (-B)  A

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◆ From: 122.117.205.246
推 dogalan:咦 原來是我最後面代入算錯 謝謝你
→ dogalan:不過為什麼 最後B跟-B要換位再轉置?
推 AIdrifter:原矩陣取transpose要A12到A21
→ AIdrifter:不好意思 不過我有一部分看不懂
→ AIdrifter:為何real smymetric保A^T=A B^T=-B 難道不可能A^T=B嗎?
→ AIdrifter:更正A^T=-B B^T=A  或者其他各種組合@@
→ cha122977:實部和虛部不會互相影響~
推 dogalan:因為B前面*i是虛部 所以不會影響到A的實部
推 AIdrifter:原來那i是虛部 我還以為是係數XDD