Matrix with only real eigenvalues

  • Thread starter Meistro
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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! :redface:

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?
 

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shmoe
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Meistro said:
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! :redface:

No, "they" are wrong.

Meistro said:
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.

Meistro said:
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.
 

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