Question

a=(1/2,0,1/3)T E是三阶单位矩阵 A=E-a*aT B=E+2a*aT 求 A *B

Answer 1

a^Ta = 1/4+1/3 = 7/12
AB
= (E-aa^T)(E+aa^T)
= E-aa^T + aa^T - aa^Taa^T
= E - (7/12) aa^T
=
41/48 0 -7/72
0 1 0
-7/72 0 101/108