Recent content by tatianaiistb

I know that these eigenvectors correspond to the eigenvalues of A-1, and these eigenvalues are the reciprocal of those given. Does anyone know how to apply the power method to A-1? Any ideas? Thanks!

Also, I found that the eigenvector corresponding to the eigenvalue 1 is [3 1]T. Still confused though... Not sure how to proceed.

Homework Statement The Markov matrix A = [.9 .3; .1 .7] has eigenvalues 1 and .6, and the power method uk=Aku0 converges to [.75 .25]T. Find the eigenvectors of A-1. What does the inverse power method u-k=A-1u0 converge to (after you multiply by .6k)? Homework Equations The...

Nevermind. I think I figured it out. Thanks for the help!

That's why I'm so confused... The only information given is the one I stated above exactly as it is worded. And I don't know of any relevant equations for solving this system. :-(

Homework Statement Convert y"=0 to a first-order system du/dt=Au d/dt [y y']T = [y' 0]T = [0 1; 0 0] [y y']T This 2x2 matrix A has only one eigenvector and cannot be diagonalized. Compute eAt from the series I+At+... and write the solution eAtu(0) starting from y(0)=3, y'(0)=4. Check...

Homework Statement Decide whether F=x2y2-2x-2y has a minimum at the point x=y=1 (after showing that the first derivatives are zero at that point). Homework Equations FxxFyy-Fxy2 The Attempt at a Solution So I found that: Fx=2xy2-2, which at point (1,1) = 0 OK Fy=2x2y-2, which...

So, if it fails one test it is sufficient to say that it is not positive definite, and viceversa? Thanks!

Homework Statement Decide for or against the positive definiteness of [2 -1 -1 -1 2 -1 = A -1 -1 2] [2 -1 -1 -1 2 1 = B -1 1 2] [5 2 1 2 2 2 = C 1 2 5] Homework Equations Each of the following tests is a necessary and sufficient condition...

Homework Statement Decide between a minimum, maximum, or saddle point for: (a) F=-1+4(ex-x)-5xsin(y)+6y2 at the point x=y=0 (b) F=(x2-2x)cos(y) with stationary point at x=1, y=pi The professor was a bit confusing, so I did it the way I remember from Calc, but am unsure of whether I...

That's what I tried doing but I'm getting a funky solution: y(0)=2=c1*[1 0]^T + c2*[0 1]^T, so this is saying that [c1 c2]^T=2 ? When I differentiate y(t) as in previous post, y'(t)=[c2*cos(t)-c1*sin(t) -c1*cos(t)-c2*sin(t)]^T y'(0)=0=[c2 -c1]^T=0 Totally lost!

Homework Statement The higher order equation y"+y=0 can be written as a unknown d/dt[y y']=[y' y"]=[y' -y] If this is du/dt=Au, what is the 2x2 matrix A? Find its eigenvectors and eigenvalues, and compute the solution THAT STARTS FROM y(0)=2, y'(0)=0. Homework Equations y'=Ay...

Ooops, so I guess I have the correct answer in a different format... Thanks all for your help!

After normalizing the vector, I'm still not getting the right answer... a=(1/2)/sqrt(3/2)=sqrt6 / 6 b=-1/sqrt(3/2)= - sqrt6 / 3 c=(i/2)/sqrt(3/2)= (sqrt6 / 6)*i The answer is supposed to be (1/sqrt6) * (1,-2,i) Where did I err again? Thanks!

[1/sqrt3 1/sqrt3 -i/sqrt3] [i/sqrt2 0 1/sqrt2]^T = 0 the first column is the hermitian, meaning the transpose of the conjugate So are my first two equations correct? How are you solving for a,b,c using the U^H*U=I? I see what you're saying about the norm... The professor kept calling it...