Let A be an nxn skew symmetric mx.(A^T=-A).(adsbygoogle = window.adsbygoogle || []).push({});

i) Show that if X is a vector in R^n then (X,AX)=0

ii) Show that 0 is the only possible eigenvalue of A

iii)Show that A^2 is symmetric

iv)Show that every eigenvalue of A^2 is nonpositive.

v)Show that if X is an eigenvector of A^2 , then so is AX

vi)With X as in v), show that the subspace W spanned by X and AX is an A-subspace.

vii)Assuming AX not= 0. let U=X/||X||, V=AX/||AX||. Show that AU=(AU,V)V and that AV=-(AU,V)U.

ix) Show if U,V,U3 , ......,Un is an orthonormal basis of R^n, then the mx of a reletive to this basis has the form (0,b,0,0....0;-b,0,0,0....0;0,0,0,a,0...0;0,0,-a,0,0....0;C some format to the end), where C is skew symmetric (n-2)x(n-2) mx.

Thanks!

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# Homework Help: Can someone help me about skew symmetric?

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