设m次多项式f(x)=a0+a1x+...+am*x^m,设A=PYP^-1,证明f(A)=Pf(Y)p^-1这是一道线代题,..
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![设m次多项式f(x)=a0+a1x+...+am*x^m,设A=PYP^-1,证明f(A)=Pf(Y)p^-1这是一道线代题,..](/uploads/image/z/8891490-66-0.jpg?t=%E8%AE%BEm%E6%AC%A1%E5%A4%9A%E9%A1%B9%E5%BC%8Ff%28x%29%3Da0%2Ba1x%2B...%2Bam%2Ax%5Em%2C%E8%AE%BEA%3DPYP%5E-1%2C%E8%AF%81%E6%98%8Ef%28A%29%3DPf%28Y%29p%5E-1%E8%BF%99%E6%98%AF%E4%B8%80%E9%81%93%E7%BA%BF%E4%BB%A3%E9%A2%98%2C..)
设m次多项式f(x)=a0+a1x+...+am*x^m,设A=PYP^-1,证明f(A)=Pf(Y)p^-1这是一道线代题,..
设m次多项式f(x)=a0+a1x+...+am*x^m,设A=PYP^-1,证明f(A)=Pf(Y)p^-1
这是一道线代题,..
设m次多项式f(x)=a0+a1x+...+am*x^m,设A=PYP^-1,证明f(A)=Pf(Y)p^-1这是一道线代题,..
当n=0、1、2..m,
A^n=(PYP^-1)^n
=PYP^-1PYP^-1...PYP^-1
=P(Y^n)P^-1
所以f(A)=a0E+a1A+a2A^2+...+amA^m
=a0PP^-1+a1PYP^-1+a2P(Y^2)P^-1+...+amP(Y^m)P^-1
=P[a0P^-1+a1YP^-1+...+am(Y^m)P^-1]
=P[a0E+a1Y+...+am(Y^m)]P^-1
=Pf(Y)P^-1
A=PYP^-1=P^1-1Y=P^0Y=Y
f(A)=f(Y)=P^0f(Y)=P^1-1f(Y)=Pf(Y)p^-1
f(A)=a0+a1A+...+am*A^m
=a0+a1PYP^-1+...+am*(PYP^-1)^m
=Pa0P^-1 +a1PYP^-1+...+am*(PYP^-1)^m
=Pa0P^-1 +...
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A=PYP^-1=P^1-1Y=P^0Y=Y
f(A)=f(Y)=P^0f(Y)=P^1-1f(Y)=Pf(Y)p^-1
f(A)=a0+a1A+...+am*A^m
=a0+a1PYP^-1+...+am*(PYP^-1)^m
=Pa0P^-1 +a1PYP^-1+...+am*(PYP^-1)^m
=Pa0P^-1 +a1PYP^-1+...+am*P^mY^mP^-m
=Pa0P^-1 +a1PYP^-1+...+am*P^m-mY^m
= Pa0P^-1 +a1PYP^-1+...+am*P^1-1^m
=PP^-1(a0 +a1Y+...+am*Y^m)
=PP^-1Pf(Y)
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