矩阵习题.线性空间V为由基函数x1=(e^at)c - 知识问答

矩阵习题.线性空间V为由基函数x1=(e^at)cos(bt),x2=(e^at)sin(bt),x3=t(e^at)c

1个回答

微分算子D在这组基下的变换为：
Dx1= ax1 - bx2
Dx2= bx1 + ax2
Dx3= x1 + ax3 - bx4
Dx4= x2 + bx3 + ax4
Dx5= x3 + ax5 - bx6
Dx6= x4 + bx5 + ax6
设微分算子D在这组基下的矩阵为A：
D(x1,x2,x3,x4,x5,x6) = (x1,x2,x3,x4,x5,x6)A
A =
a b 1 0 0 0
-b a 0 1 0 0
0 0 a b 1 0
0 0 -b a 0 1
0 0 0 0 a b
0 0 0 0 -b a

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