Question

A是2*2矩阵,A=(a b;c a+2)是正交矩阵,则参数a,b,c满足条件

Answer 1

A是正交矩阵的充分必要条件是 AA^T=E.

AA^=

a^2+b^2 ac+(a+2)b

ac+(a+2)b (a+2)^2+c^2

所以 a,b,c 满足

a^2+b^2=1

(a+2)^2+c^2=1

ac+(a+2)b=0