Matrix with only real eigenvalues

[Meistro]

Please help me I am hopelessly lost and don't even know where to start! I guess they're right when they said girls suck at math! It's not fair!

Let A be an nxn matrix with only real eigenvalues. Prove that there is an orthogonal matrix Q such that (Q^T)AQ is upper triangular with eigenvalues along the main diagonal.


Any of you boys out there help me solve this?

 

[shmoe]

Please help me I am hopelessly lost and don't even know where to start! I guess they're right when they said girls suck at math! It's not fair!

No, "they" are wrong.

Let A be an nxn matrix with only real eigenvalues. Prove that there is an orthogonal matrix Q such that (Q^T)AQ is upper triangular with eigenvalues along the main diagonal.

You can use induction on n. For a hint on the induction step, you can try to find an orthogonal matrix P where (P^T)AP is 1 step closer to being upper triangular- try to get the first column in the right shape.

Any of you boys out there help me solve this?

Girls can excel at math just as well as boys, you shouldn't exclude a potential source of aid.