Question

if A is a nilpotent matrix of order p,then find the inverse of the matrix I+A and I-A

Answer 1

@UnkleRhaukus come help this brother here; I forgot how to do matrix

Answer 2

i can't remember linear algebra at the momnet

Answer 3

Me neither.

Answer 4

According to this site, near bottom, \[(I+A)^{-}= I-N+N^2-N^3+....\] http://en.wikipedia.org/wiki/Nilpotent_matrix

Answer 5

and according to my note, my prof said that
\[(I-N)^{-}=I+N+N^2+N^3+....\]

Answer 6

his argument is
\[\frac{1}{x}=1+x+x^2+x^3+....\]
\[\frac{1}{I-A}=(I-A)^{-} = I+A+A^2+A^3+...\]like what I write above. hehehe...everything doesn't relate to me.

Answer 7

\[\left[ I-A \right]^{-1}=\frac{ I }{ I-A }=I+A+A^2+...+A^{p-1}+\frac{ A^p }{ I-A }\]and \[A^p=[0]\]Then,\[\left[ I-A \right]^{-1}=I+\sum_{k=1}^{p-1}A^k\]