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quadric transformation proof

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Hello this hasn't anything to do with game creation, but i don't know where else i could ask. This is a part of my current 'homework' i can't solve: Given is a Quadric with Todo: Show that there exists an orhogonal Matrix and scalars with for We have used lambda_i for the eigenvalues of a Matrix, but i don't even know where to start this proof. I would appreciate your help. Thanks in advance.

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I have an idea of where you might look for information on this particular problem, but first you may need to clarify what you mean by 'homework' (due to the forum's policy on homework-related questions).

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