Let $A$ be an $n\times n$ matrix with real elements so that $I+A$ and $I-A$ are nonsingular and $B=(I−A)(I+A)^{−1}$ is orthogonal. Is $A$ skew symmetric?
How to prove that if $I+A$ and $I-A$ are nonsingular and $(I−A)(I+A)^{−1}$ is orthogonal then $A$ is skew symmetric?
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0Did you mean $B=(I−A)(I+A)^{−1}$ or $B=(I−A)((I+A)^{−1})$ ? – 2017-01-05
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0what did you try? – 2017-01-05
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0until now i have that $xtAx=0$ – 2017-01-05
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0I think you mean $$x^tAx=0$$ – 2017-01-05
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0That's a good point. You can prove that $A$ is skew simmetric from that. – 2017-01-05
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0thank you so much! i got this now – 2017-01-05