yeland404
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Homework Statement
a square matrix A with ker(A^2)= ker (A^3), is ker(A^3)= ker (A^4),verify...
micromass said:What did you try already??
yeland404 said:it means that A^2*vector x= 0 and A*x=0 has same result,then I really confused how to do the next step
micromass said:No, it means that
A^2x=0~\Leftrightarrow~A^3x=0
You need to prove that
A^3x=0~\Leftrightarrow~A^4x=0
yeland404 said:emm..., to the difinition it says that ker(A) is T(x)=A(x)=0
micromass said:Yes, but you're not working with ker(A) here, but with ker(A2).
yeland404 said:should define a matrix A and write A^2 as dot product of A & A,and also to A^3...it seems to be so complex, or use the block to divide the matrix into some small matrix?
micromass said:Do you understand my Post 4??
yeland404 said:so times A on both side of the equation?