(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

T a linear operator on inner product space V and W a T-invariant subspace of V. ThenifT is self-adjointthenTw is self-adjoint.

2. Relevant equations

Thm: T is self-adjoint iff [tex]\exists[/tex] an orthonormal basis for V consisting of e-vectors of T.

3. The attempt at a solution

Let [tex]\beta[/tex]1 be a basis for Tw and by thm can extend to a basis [tex]\beta[/tex] for V, s.t. [tex]\beta[/tex]1[tex]\subseteq[/tex][tex]\beta[/tex]. But by above thm, [tex]\beta[/tex] is ON and consists of e-vectors of T, so then [tex]\beta[/tex]1 is also ON and consists of e-vectors of T, and Tw is self-adjoint.

Does my proof make any sense?? Thanks everyone!

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# Homework Help: Self-Adjoint Operators problem

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