Determine the null space and rank

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Reference no: EM131760969

Question: (Eigenvectors of a symmetric 2 × 2 matrix) Let p, q ∈ Rⁿ be two linearly independent vectors, with unit norm (||p||₂ = ||q||₂ = 1). Define the symmetric matrix A ? pq^? + qp^?. In your derivations, it may be useful to use the notation c ? p^?q.

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.

Reference no: EM131760969

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