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 2007-07-16, 15:33 #1 buan   Jul 2007 2 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 (I-A) thanks,
2007-07-16, 16:44   #2
R.D. Silverman

Nov 2003

746010 Posts

Quote:
 Originally Posted by buan 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 (I-A) thanks,
Hint:

Simply expand I/(I-A) and ask what are the requirements for convergence?

 2007-07-16, 16:57 #3 masser     Jul 2003 Behind BB 23·32·52 Posts Another hint: What is (I-A)*(I+A+A^2+A^3+....) ? To reiterate what Dr. Silverman says above, you do need to show that the series converges...
 2007-07-17, 15:07 #4 buan   Jul 2007 28 Posts Thank you for the hint Prof. it really help....

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