Solved: 2326 deal with the eigenvalue/eigenvector problem for n n real skew-symmetric
Chapter 7, Problem 23(choose chapter or problem)
2326 deal with the eigenvalue/eigenvector problem for n n real skew-symmetric matrices.Let A be an n n real skew-symmetric matrix.(a) Prove that for all v1 and v2 in Cn,Av1, v2 = v1, Av2,where , denotes the standard inner product inCn. [Hint: See Lemma 7.5.9.](b) Prove that all nonzero eigenvalues of A are pureimaginary ( = ). [Hint: Model your proofafter that of (1) in Theorem 7.5.4.]
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