Question

(二-B3)求解一道线性代数题,如图

Answer 1

任意矩阵 A

H = (A + A^T) / 2 是对称阵,K = (A - A^T) / 2 是反对称阵.

且 A = H + K

若表示不唯一：A = H + K = H' + K'

则：H - H' = K' - K

H - H' 是对称阵,K' - K 是反对称阵.

对称阵 = 反对称阵,则只能说明它们都是 0 矩阵.

H - H' = K' - K = 0,也就是 H = H',K = K