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Matrix Algebra Find an inverse for I-A

  • #1
Suppose A^n=0 for some n>1. Find an inverse for I-A.

I don't understand how to do this. It isn't homework, but I'm just studying.
 

Answers and Replies

  • #2
Dick
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If r were a real number with |r|<1 then 1/(1-r)=1+r+r^2+r^3+... It's a geometric series. Substitute r=A and see what you can conclude. Then prove it's true.
 
  • #3
HallsofIvy
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Or, essentially the same thing,
[tex]I- A^n= (I- A)(I+ A^2+ A^3+ \cdot\cdot\cdot+ A^{n-1})[/tex]

And, of course, since [itex]A^n= 0[/itex], [itex]I- A^n= ?[/itex]
 

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