A matrix A Cnxn is called skew-Hermitian if A* = -A. Show that skew-Hermitian matrices...

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A matrix A € Cnxn is called skew-Hermitian if A* = -A. Show that skew-Hermitian matrices have only purely imaginary eigenvalues, i.e., any eigenvalue of a skew-Hermitian matrix has the form λ = aż with a € R. Hint: Consider the Schur decomposition, and see what it means that A* = —A. A matrix A € Cnxn is called skew-Hermitian if A* = -A. Show that skew-Hermitian matrices have only purely imaginary eigenvalues, i.e., any eigenvalue of a skew-Hermitian matrix has the form λ = aż with a € R. Hint: Consider the Schur decomposition, and see what it means that A* = —A.

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Solution we have given Afchxn where A A ul A is Skew Hermition matrix qe Now since A is Skew H... View the full answer