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## Homework Statement

T a linear operator on inner product space V and W a T-invariant subspace of V. Then

**if**T is self-adjoint

**then**Tw is self-adjoint.

## Homework Equations

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

## 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!