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Multiplicity of an eigen value , k = dim[ Null(T  k I)^( dim V) ] 
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#1
Feb1613, 09:25 AM

P: 53

I have been reading Linear Algebra done right by Sheldon Axler
I got two conceptual queries : (1) It states that for a Matrix of an operator T = [ 5 1 ; 0 5 ] ( ; indicates next row ) that dim Null [ (T  5 I )^{2} ] = multiplicity of the eigen value 5 = 2 However, T  5 I= [ 0 1 ; 0 0 ] and (T  5I )^{2} = [ 0 0 ; 0 0 ] dim Null [ (T  5 I )^{2} ] ≠ 2 I am a bit confused about the given result in the book hence. Could anyone please clarify. (2) Multiplicity of an Eigen value , k = dim[ Null(T  k I)^{dim V} ] I have been trying to prove this without induction . Any direction please ? thanks 


#2
Feb1613, 12:22 PM

Mentor
P: 18,044




#3
Feb1613, 01:14 PM

P: 53

Thanks a lot micromass. I will do the needful



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