April 28th, 2009, 07:02 AM  #1 
Newbie Joined: Apr 2009 Posts: 28 Thanks: 0  Matrix Problem
Hi, I need some help to solve the following problem. Let A be any 2 x 2 matrix over C and let f(x) = a0 + a1x + a2.x^2 + ..... + an.x^n be any polynomial over the complex numbers C. Show that f(A) is a matrix which can be written as c1.I + c2.A for some c1, c2 belongs to C, where I is the identity matrix. Can somebody help me how to start it? Thanks in advance! 
April 28th, 2009, 10:13 AM  #2 
Senior Member Joined: May 2008 From: York, UK Posts: 1,300 Thanks: 0  Re: Matrix Problem
If you can show it for any then you can show it for an arbitrary polynomial Then, show that it is possible to write as , and then show by induction that it is possible for any 
April 28th, 2009, 07:57 PM  #3 
Senior Member Joined: Jul 2008 Posts: 144 Thanks: 0  Re: Matrix Problem
the degree of minimal polynomial of is less then 2. so in polynominal ring 
April 29th, 2009, 05:49 AM  #4  
Senior Member Joined: May 2008 From: York, UK Posts: 1,300 Thanks: 0  Re: Matrix Problem Quote:
 

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