search for: e_2

...problem can be solved by linear programming, so I include code for my attempt at this via RGLPK. It says that there is no feasible solution, but the solution is known analytically in the case below. Here is the precise problem: Minimise, over 100?1 real vectors v, Max_i(|v_i|) such that X'v=e_2, where X is a given 100?2 matrix and e_2 =(0,1)'. The v_i are the elements of v. I have put the actual X matrix at the end of this post, along with a feasible starting value for v. The correct minimum is 0.01287957, obtained with v_i=0.01287957 for i<=50 and v_i = 0.01287957 for i>=5...

Hi, It is my understanding that the eigenvectors of a circulant matrix are given as follows: 1,omega,omega^2,....,omega^{p-1} where the matrix has dimension given by p x p and omega is one of p complex roots of unity. (See Bellman for an excellent discussion on this). The matrix created by the attached row and obtained using the following commands indicates no imaginary parts for the