U,Vand W are finite dimensional vector spaces and linear transformation $T:U to V , S:V to W And P:W to U $
I can only understand from here R(T)+N(T)=Dim(U) and R(S)+N(S)=Dim(V)by Rank-Nullity Theorem and R(T)=R(S) are equal .Hence, Dim(U)-N(T)=Dim(V)-N(S). I don't know how to proceed further.
linear-algebra linear-transformations
asked Dec 26 '18 at 19:32
sejy
1029
add a comment |
I can only understand from here R(T)+N(T)=Dim(U) and R(S)+N(S)=Dim(V)by Rank-Nullity Theorem and R(T)=R(S) are equal .Hence, Dim(U)-N(T)=Dim(V)-N(S). I don't know how to proceed further.
linear-algebra linear-transformations
asked Dec 26 '18 at 19:32
sejy
1029
add a comment |
I can only understand from here R(T)+N(T)=Dim(U) and R(S)+N(S)=Dim(V)by Rank-Nullity Theorem and R(T)=R(S) are equal .Hence, Dim(U)-N(T)=Dim(V)-N(S). I don't know how to proceed further.
linear-algebra linear-transformations
asked Dec 26 '18 at 19:32
sejy
1029
I can only understand from here R(T)+N(T)=Dim(U) and R(S)+N(S)=Dim(V)by Rank-Nullity Theorem and R(T)=R(S) are equal .Hence, Dim(U)-N(T)=Dim(V)-N(S). I don't know how to proceed further.
linear-algebra linear-transformations
linear-algebra linear-transformations
asked Dec 26 '18 at 19:32
sejy
1029
asked Dec 26 '18 at 19:32
sejy
1029
asked Dec 26 '18 at 19:32
sejy
1029
asked Dec 26 '18 at 19:32
sejy
1029
asked Dec 26 '18 at 19:32
sejy
1029
1029
add a comment |
add a comment |
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