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Math Help - singular

  1. #1
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    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
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  2. #2
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    Quote Originally Posted by prashantgolu View Post
    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


    What's your definition of "singular"??

    Tonio
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  3. #3
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    By singular I mean that it is either left invertible or right invertible...but not both sided...
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  4. #4
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    Quote Originally Posted by prashantgolu View Post
    By singular I mean that it is either left invertible or right invertible...but not both sided...

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

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

    Tonio
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