1. ## singular

if V is a finite dimensional over F and T belong to A(V)
T is singulare iff there exists v not equal to zero...such that vT=0

please prove the reverse part....that is if vT=0 then T is singular
Thanks

2. Originally Posted by prashantgolu
if V is a finite dimensional over F and T belong to A(V)
T is singulare iff there exists v not equal to zero...such that vT=0

please prove the reverse part....that is if vT=0 then T is singular
Thanks

Tonio

3. By singular I mean that it is either left invertible or right invertible...but not both sided...

4. Originally Posted by prashantgolu
By singular I mean that it is either left invertible or right invertible...but not both sided...

Weird definition...but never minds: if $\displaystyle T$ were invertible then there'd exist $\displaystyle S\in A(V)$ s.t. $\displaystyle ST =TS=I$ , with I = the identity

(operator or matrix, it never minds), and then $\displaystyle 0=Tv\Longrightarrow 0 = Sv = STv=Iv= v\Longrightarrow v=0$

Tonio