Recent content by aznkid310

Each of the three eigenvalues (zero) in the min. poly could have jordan blocks of size 1,2, or 3. So: [0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0] [0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]...

Right, so for example: [0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0] [0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]

Thanks HallsofIvy. So using this info, we can have possible jordan blocks of size 1,2, or 3. So the possible matrices are: [0 1 0 0 0 1 0 0 0] [0 0 0 0 0 0 0 0 0] [0 1 0 0 0 0 0 0 0] Where I can fill out the rest of the 6x6 with zeros if I wanted the original matrix. My question is, why...

If the min poly is p(s) = s^3, doesn't that mean that only three of the six are zero? How would I find the other 3 eigenvalues? I must not be understanding this correctly. I understand that the matrix needs to be 6x6, but I only know 3 of the eigenvalues? I guess if I understand the first...

Homework Statement Suppose that A is a 6x6 matrix with real values and has a min. poly of p(s) = s^3. a) Find the Characteristic polynomial of A b) What are the possibilities for the Jordan form of A? c) What are the possibilities of the rank of A? Homework Equations See below...

Fixed Thanks.

Homework Statement Let a be all real numbers, nxn. Prove that a) rank(A) less than or equal to rank(exp(A)) b) rank(exp(A)-I) less than or equal to Rank(A) Homework Equations I'm new to math proofs and so don't really know where to start. Could someone point me in the right direction? Would...

Yes that's what I thought. Reading a little furthur, it seems that I should find the eigenvectors of phi(t), then do: ln(phi(t)) = V*ln(inv(V)*phi(t)*V)*inv(V), where V is the matrix of eigenvectors. But phi(t) is not diagonalizable, so I don't know how to proceed from here.

Thanks for the reply Mark44. How do we deal with the ln(0) terms?

Homework Statement So the first part of the problem asks us to solve for the state transition matrix, which I found to be: Phi(t) = [2 0 0; (2-e^-t) e^-t 0; 0 0 e^-2t]; I need to find the matrix A, which I assume can be done with the following relation: Phit(t) = e^(At) where A is also a...

Homework Statement A system has damping ratio 0.5, natural freq. 100 rad/s, DC gain of 1. Find the response of the system to a unit step input. Homework Equations Im having trouble doing the partial fraction expansion. The Attempt at a Solution I have attached a word document...

well, expanding the series out, it appears that it is indeed positive throughout the interval and uniformly increasing, so x_max =1. Then f''(x)_max = f''(1) = ((1^2-2+2)*exp(1)-1)/(1^3) = 1.718281828 ? Thus, h = 0.0083568657 1/h = 119.66 ~120 So the # of intervals N = 120? (ie 0 to...

Trying the Taylor Series: f = (exp(x)-1)/x = sum (n=0 to infinity) (x^n)/(n+1)! f'' =[n(n-1)x^(n-2)]/(n+1)! How do I evaluate this to find the max value?

Homework Statement Use the composite trapezoidal sum rule to evaluate I = integral from 0 to 1 of: (exp(x)-1)/x At x = 0 the integrand evaluates to 1. Select the step size h in order to guarantee an approximation error less than 10e-5. Carry out your calculation with at least 10 decimal...

it took 5 iterations, which should be correct since it is less than the 'power' method