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Math Help - Linear algebra toughy

  1. #1
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    Linear algebra toughy

    Suppose that n is a positive integer. Define T \ in L(F^n) by:

    T( z_1, ....., z_n)=(0, z_1,...., z_n-1).

    Find a formula for T*( z_1, ....., z_n).

    T*is the adjoint of T.
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  2. #2
    Grand Panjandrum
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    Quote Originally Posted by mathisthebestpuzzle View Post
    Suppose that n is a positive integer. Define T \ in L(F^n) by:

    T( z_1, ....., z_n)=(0, z_1,...., z_n-1).

    Find a formula for T*( z_1, ....., z_n).

    T*is the adjoint of T.
    The adjoint is defined by the relation:

    \langle T^*(\bold{v}),\bold{w}\rangle = \langle \bold{v},T(\bold{w}) \rangle = v_2w_1+ ... + v_nw_{n-1}

    Therefore:

     T^*(v_1, v_2, ..., v_n)=(v_2, v_3, .., v_n, 0)

    You can get the same result by constructing the matrix if T and taking its transpose.

    RonL
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