gram_schemidt.m

求矩阵特征值和特征向量的算法：QR算法。用于线性方程组的求解

function [Q,R]=Gram_Schemidt(A)
[m,n]=size(A);beta=zeros(m,n);R=zeros(m,n);
R(1,1)=norm(A(:,1),2);
beta(:,1)=A(:,1)/R(1,1);
Q=[beta(:,1)];
for j=2:n
    for k=1:j-1
    R(k,j) =beta(:,k)'*A(:,j);
    beta(:,j)=A(:,j)-R(k,j)*beta(:,k);
    A(:,j)=beta(:,j);
    end
    R(j,j)=norm(beta(:,j),2);
    beta(:,j)=beta(:,j)/R(j,j);
    Q=[Q beta(:,j)];    
end
end
% clc
% clear
% A=[5 -2 -5 -1;1 0 -3 2;0 2 2 -3;0 0 1 -2];
% [Q,R]=Gram_Schemidt(A)