Linear Algebra and the C Language/a0oj

__NOTOC__ E1**2 b1r1 + E2**2 b2r2 + E3**2 b3r3 = A**2 Copy/Paste into the octave window % A property of spectral decomposition: % % E1**2 * b1r1 + E2**2 * b2r2 + E3**2 * b3r3 = A**2 % E1**3 * b1r1 + E2**3 * b2r2 + E3**3 * b3r3 = A**3 % ... % E1**n * b1r1 + E2**n * b2r2 + E3**n * b3r3 = A**n % % We can calculate the nth power of A by taking % the nth power of each of the eigenvalues. % % 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) % % E : The eigenvalues of A. % % 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); Evalues = diag([Evalues]); E1 = Evalues(1); E2 = Evalues(2); E3 = Evalues(3); E1_2_b1r1 = E1^2.*V1*V1'; E2_2_b2r2 = E2^2.*V2*V2'; E3_2_b3r3 = E3^2.*V3*V3'; A_2 = E1_2_b1r1 + E2_2_b2r2 + E3_2_b3r3 A_2= A^2 %%