Linear Algebra and the C Language/a0oh

__NOTOC__ b1r1**2 = b1r1; ... ... ... b1r1**3 = b1r1; ... ... ... b1r1**P = b1r1; Copy/Paste into the octave window % A property of spectral decomposition: % % The b*r* are projectors. For example, if I project point P onto the x-axis, % P is on the x-axis. Once P is on the x-axis, I can project it an infinite % number of times onto the x-axis, and it will not move. % This is materialized in our case by the fact : % % b1r1**2 = b1r1 % b1r1**3 = b1r1 % b1r1**4 = b1r1 % ... % b1r1**n = b1r1 % % V (b) : The columns of the eigenvectors of A % V'(r) : The rows of the eigenvectors of the inverse of A % (Here the transpose: see the first example). % % V1V1' (b1r1) is obtained by multiplying the first column of the eigenvector % of A by the first row of the eigenvector of the inverse of A clear, clc A = round(10*randn(3)); %% A matrix 3x3 A = A'*A; %% A symetric matrix % Eigenvectors, Eigenvalues [Evectors,Evalues] = eigs(A); V1 = Evectors(:,1); V2 = Evectors(:,2); V3 = Evectors(:,3); b1r1_2 = (V1*V1')^2 b1r1_4 = (V1*V1')^4 b1r1_6 = (V1*V1')^6 %%