5.Consider the eigenvalues given by equation (39). Show that (σ1X+σ2Y)2−4(σ1σ2−α1α2)XY=(σ1X−σ2Y)2+4α1α2XY.σ1X+σ2Y2−4σ1σ2−α1α2XY=σ1X−σ2Y2+4α1α2XY. Hence conclude that the eigenvalues can never be complex-valued.

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