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    Restriction to an eigenspace

    E-HK-64-3

    Area
    Algebra
    Topics
    Characteristic Values, Invariant Subspaces, Linear Algebra
    Status
    draft

    Let \(c\) be a characteristic value of \(T\) and let \(W\) be the space of characteristic vectors associated with the characteristic value \(c\). What is the restriction operator \(T_W\)?

    Solution

    By definition, \[ W=\ker(T-cI). \] Thus every \(w\in W\) satisfies \(Tw=cw\). Therefore the restriction is simply \[ T_W=cI_W. \]

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