Re: [理工] [線代]-成大96

[CRAZYAWIND (考試快到了!!)]

※ 引述《dendrobium (石斛蘭)》之銘言：
: 成大96 計算機數學
: 1. A matrix A is said to be skew symmetrix if A^T = -A.
:    Let A be an nxn skew symmetrix matrix.
:   (a) If A=B+C where B is symmetric and C is skew symmetric, find B and C.
:   (b) If n is odd, show that A must be singular.
: 這題感覺不難
: 可是確不知道該怎麼下筆Orz
: (B+C)^T = -A
: B^T - C = -A
: B^T = C - A
: 所以 b_ij = c_ij-a_ij <= 應該不是要這種答案吧@@?


A = B + C
    A +  A^T       A - A^T
A = ─────  + ─────
        2             2

  =    B        +   C


因為A^T = -A
      -A + A
B = ──────  = 0
         2
      A + A
C = ─────    = A = -A^T
        2

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