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I have an upper triangular matrix for an operator T in which an eigen value has been repeated s times in total.

Derive an expression for s .

My thoughts : ( Let * imply contained in )

then :I know that :

(a)

Null T^{0}* Null T^{1}*.....*Null T^{dim V}= Null T^{dim V + 1}= ........

(b) Will i have to investigate the effect of higher powers of ( T - k I ) where k is the intended eigen value ??

(c) the book which i am reading : Sheldon Axler's Linear Algebra hasn't introduced Jordan form as of now.

Any direction for this will be appreciated. Thanks

Can i prove it from these results ?

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# Derive an expression to find how many times an eigen value is repeated

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