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Math Help - normal, self-adjoint or neither...

  1. #1
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    normal, self-adjoint or neither...

    I need to prove whether the following linear operator is normal, self-adjoint, or neither, and if possible, to find an orthonormal basis of eigenvectors of T for V and the corresponding eigenvalues
    Let V = \mathbb{R}^2 be an inner product space, let T be defined by T(a,b) = (2a-2b,-2a + 5b)

    No idea how to do this ,any help please? thanks
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  2. #2
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    Krizalid's Avatar
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    find the associated matrix respect to the standard basis for \mathbb R^2.

    T is normal if T\cdot T^*=T^*\cdot T, self-adjoint if T=T^*.

    find T^*, in order to do that, you're gonna have to get the associated matrix, but since we're working on real numbers, T^* is just T^t.

    as for the eigenvalues and eigenvectors, that's a quite straightforward work, and i got no time no help ya there, so i hope someone's gonna provide help there.
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