Question: Let p, q R n be two linearly independent vectors, with unit nor Define the symmetric matrix In your derivations, it may be useful
Let p, q ∈ Rn be two linearly independent vectors, with unit nor
Define the symmetric matrix 
In your derivations, it may be useful to use the notation 
1. Show that p + q and p – q are eigenvectors of A, and determine the corresponding eigenvalues.
2. Determine the null space and rank of A.
3. Find an eigenvalue decomposition of A, in terms of p, q.
4. What is the answer to the previous part if p, q are not normalized?
(||P||2 = ||9||2 = 1).
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1 We have from which we obtain Thus u p q is an unnormalized eigenvector of A with eigenvalue c 1 2 ... View full answer
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