Recent content by JerryKelly

anyone know,please?

http://www.geocities.com/gotoyourhouse88/qiangzhe/untitled.JPG

I figured it out already.

your way is seeing better than my way. Thanks,agian! It is very helpful.

Thanks for help,HallsofIvy! It made perfert sence! for the first step, it is so similar what i was doing. I was doing ABx=BAx=B\lambdax=\lambdaBx. since A(Bx)=\lambda(Bx) Bx=0 or Bx is eigenvector.

why you cannot help me?

Let A be an nxn mx with n distinct eigenvalues and let B be an nxn mx with AB=BA. if X is an eigenvector of A, show that BX is zero or is an eigenvector of A with the same eigenvalue. Conclude that X is also an eigenvector of B. I could show BX is zero or is an eigenvector of A with the...

If A is a symmetric nxn mx of rank<=r>=1 and X is a unit eigenvector of A, with eigenvalue [SIZE="4"]a not= 0, let B=A - aXX^T. Show that B is symmetric and that N(A) is a proper subspace of N(B). Conclude that rank B=<r-1. i could show X is in N(B) but not in N(A). Does anyone know how I can...

Could you solve the last two parts by using this definition for me,please? I have no any idea for the last two parts. Thanks!

Yes,it is homework question. So far, I just have a idea for part iv), and I have no idea for the rest of them. For part iv), i can use (AX,X)=(X,-AX)=-A(X,X). Except this one, I have no idea how to do the rest of them. Could you give me some help,please? Thanks!

Let A be an nxn skew symmetric mx.(A^T=-A). 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...