Show that A (symmetric but complex) has only one line of eigenvectors: A = [~ _~] is not
Chapter 6, Problem 15(choose chapter or problem)
Show that A (symmetric but complex) has only one line of eigenvectors: A = [~ _~] is not even diagonalizable: eigenvalues A = 0, O. AT = A is not such a special property for complex matrices. The good property is AT = A (Section 10.2). Then all A'S are real and eigenvectors are orthogonal.
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