# Math Help - self-adjoint linear operator

If T:V->V is a self-adjoint linear transformation, V is a finite-dimensional inner product space over C, how can I prove that T has n distinct eigenvalues?

2. Originally Posted by guin
If T:V->V is a self-adjoint linear transformation, V is a finite-dimensional inner product space over C, how can I prove that T has n distinct eigenvalues?

That is false, choose for example $T=I$ (the identity map) and $n\geq 2$ .

Fernando Revilla