进一个球好难
春芽
共回答了15个问题采纳率:86.7% 举报
1,
0 = AB,0 = A^(-1)*0 = A^(-1)AB = [A^(-1)A]B = B.
2,
AX = AY,
X = [A^(-1)A]X = A^(-1)[AX] = A^(-1)[AY] = [A^(-1)A]Y = Y
3,
(A+B)(A-B) = A^2 + BA - AB - B^2,
BA = AB时,
(A+B)(A-B) = A^2 + BA - AB - B^2 = A^2 - B^2.
4,
[A+A^T]^T = A^T + [A^T]^T = A^T + A = [A+A^T]
[A-A^T]^T = A^T - [A^T]^T = A^T - A = -[A-A^T]
所以,
A+A^T是对称矩阵,A-A^T是反对称矩阵
5,
A = [(A/2)+(A/2)^T] + [(A/2)-(A/2)^T]
而,
[(A/2)+(A/2)^T]^T = (A/2)^T+[(A/2)^T]^T = (A/2)^T + (A/2) = [(A/2)+(A/2)^T],[(A/2)+(A/2)^T]是对称矩阵.
[(A/2)-(A/2)^T]^T = (A/2)^T-[(A/2)^T]^T = (A/2)^T - (A/2) = -[(A/2)-(A/2)^T],[(A/2)-(A/2)^T]是反对称矩阵.
因此,
A可以表示成1个对称矩阵和1个反对称矩阵之和
1年前
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