Left and Right Eigenvectors with Distinct Eigenvalues
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Let A belonging to C^nxn be a skew-hermitian.
a) Prove directly that the eigenvalues of A are purely imaginary.
b) Prove that if x and y are eigenvalues associated to distinct eigenvalues, then they are orthogonal, i.e. x^H*y = 0
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Solution Summary
In this solution, we prove that if A is a complex-valued square matrix with right eigenvector x and corresponding eigenvalue lambda as well as another condition detailed within, then y^H x = 0.
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