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Let V be a vector space and T: V->V be a linear map such that T^2=T. 1) Prove that lm(T)=ker(Id-T) 2) Prove that V=ker(T)⊕Im(T)

Let V be a vector space and T: V->V be a linear map such that T^2=T. 1) Prove that lm(T)=ker(Id-T) 2) Prove that V=ker(T)⊕Im(T)

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ISBN:9781305658004
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Chapter5: Inner Product Spaces
Section5.CM: Cumulative Review
Problem 24CM
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Let V be a vector space and T: V->V be a linear map such that T^2=T.

1) Prove that lm(T)=ker(Id-T)

2) Prove that V=ker(T)⊕Im(T)

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