20070716, 15:33  #1 
Jul 2007
2_{8} Posts 
[Need help] about Matrix Polynomial
Can any one give a hint...
I want to prove that for Matrix A if all of its eigenvalue is less than one in magnitude ( eigenvalue < 1 ), then: I + A + A^2 + A^3 + ... = inverse of matrix (IA) thanks, 
20070716, 16:44  #2  
Nov 2003
2^{2}×5×373 Posts 
Quote:
Simply expand I/(IA) and ask what are the requirements for convergence? 

20070716, 16:57  #3 
Jul 2003
wear a mask
624_{16} Posts 
Another hint: What is (IA)*(I+A+A^2+A^3+....) ?
To reiterate what Dr. Silverman says above, you do need to show that the series converges... 
20070717, 15:07  #4 
Jul 2007
2 Posts 
Thank you for the hint Prof. it really help....

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