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sanctifier
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Let T is a linear transformation from a vector space V to V itself. The dimension of V, denoted by dim(V), is finite.
If the rank of T, denoted by rk(T), is equivalent to the rank of TT, i.e., rk(T)=rk(TT)
why is the intersection of image of T(denoted by im(T)) and the kernel of T(denoted by ker(T)) is the zero vector, i.e., im(T)[tex]\cap[/tex]ker(T)={0}?
Thanks for any help.
If the rank of T, denoted by rk(T), is equivalent to the rank of TT, i.e., rk(T)=rk(TT)
why is the intersection of image of T(denoted by im(T)) and the kernel of T(denoted by ker(T)) is the zero vector, i.e., im(T)[tex]\cap[/tex]ker(T)={0}?
Thanks for any help.