411 REFERENCE · Wikibooks
Linear Algebra and the C Language/a0oi
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b1r1 * b3r3 = 0; ... ... ... b1r1 * b2r2 = 0; ... ... ... b2r2 * b3r3 = 0;
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% A property of spectral decomposition:
%
% b1r1 * b2r2 = 0
% b1r1 * b3r3 = 0
% b2r2 * b3r3 = 0
%
% This simply materializes that our projectors are orthogonal to each other.
%
% 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_b2r2 = (V1*V1')*(V2*V2')
b1r1_b3r3 = (V1*V1')*(V3*V3')
b2r2_b3r3 = (V2*V2')*(V3*V3')
%%