Recent content by angelz429

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    Approximate Eigenvalues for [4 3] [3 5]

    Well, since no one can help... :( I don't need it anymore, thanks for looking!
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    Graduate Positive Definite Matrices eigenvalues

    So I made a mistake, and I figured it out. It's not like I can delete them. I have already posted to homework, and gotten it solved. Thanks though.
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    Are All Eigenvalues of a Matrix Between Defined Limits?

    Thanks!
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    Are All Eigenvalues of a Matrix Between Defined Limits?

    ahhh nevermind... i got it!
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    Are All Eigenvalues of a Matrix Between Defined Limits?

    Alright, so I understand the first part... now how do I use this to show that all the eigenvalues of B are between zero & eight? I just checked that B is positive definite...
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    Solving Nilpotent Matrices: Invertibility of I+N

    Thanks!
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    Are All Eigenvalues of a Matrix Between Defined Limits?

    errr i mean that alpha - lambda is > 0
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    Are All Eigenvalues of a Matrix Between Defined Limits?

    oh riiiight! Thanks!... but how can we guarantee that alpha + lambda is > 0?
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    Solving Nilpotent Matrices: Invertibility of I+N

    so how does this show that I + N is invertible?
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    Solving Nilpotent Matrices: Invertibility of I+N

    P(n) approaches 1/(1+0) = 1
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    Solving Nilpotent Matrices: Invertibility of I+N

    yes... Let P(n) = 1-x+x^2-x^3+x^4-...+x^n xP(n) = x-x^2+....-x^n+x^(n+1) add them (x+1)P(n)=1+x^(n+1) therefore P(n)=1+x^(n+1)/(x+1) which goes to 1/(1+x)
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    Are All Eigenvalues of a Matrix Between Defined Limits?

    ok, so det(A-lambda*I-alpha*I) implies det (A-alpha*lamba*I) therefore alpha is an eigenvlaue od A-lambda*I and alpha*lambda is an eigenvalue of A. But what does this say about the relationship between alpha and lambda? I'm supposed to see that if alpha > lambda A is positive definite & is...
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    Solving Nilpotent Matrices: Invertibility of I+N

    ok well we know: P(n) = 1 + x + ... + x^n xP(n) = x + x^2 + ... + x^n + x^(n+1) (x-1)P(n)=x^(n+1)-1 P(n) = x^(n+1)-1/(x-1) goes to -1/(x-1) = 1/(1-x) <== close to 1/(1+x) if you use -x, P(n)= 1/(1+x) because the MacLaurin series for 1/(1+x) f(x) = f(0) + f'(0)x + f''(0)x^2...
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    Are All Eigenvalues of a Matrix Between Defined Limits?

    like any other eigenvalue i suppose do det((A-lambda*I)-alpha*I)=0 and solve for alpha.
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    Are All Eigenvalues of a Matrix Between Defined Limits?

    hmm... i understand what you are saying, but I'm not sure how to apply it. My main problem is with proving part a.