Question

matlab任意生成一个实矩阵 用household变换成下三角矩阵（在线等）

Answer 1

function [Q,R]=Householder(A)

[m,n]=size(A); %要求m>=n;

V=zeros(m);

Q=eye(m);

R=zeros(m,n);

a=zeros(m,n);

for k=1:n

P=eye(m);

I=eye(n-k+1);

x=A(1:n-k+1,n-k+1);

e=zeros(n-k+1,1);

e(n-k+1,1)=1;

V(1:n-k+1,k)= sign(x(n-k+1))*norm(x)*e+x;

V(1:n-k+1,k)=V(1:n-k+1,k)/norm(V(1:n-k+1,k));

F=I-2*V(1:n-k+1,k)*V(1:n-k+1,k)';

P(1:n-k+1,1:n-k+1)=F;

Q=Q*P; A(1:n-k+1,1:n-k+1)=A(1:n-k+1,1:n-k+1)-2*V(1:n-k+1,k)*(V(1:n-k+1,k))'*A(1:n-k+1,1:n-k+1);

end

R=A;

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