matlab编写施密特正交分解算法求矩阵A的特征值和特征向量

以下是Matlab代码实现施密特正交分解算法求矩阵A的特征值和特征向量：

function [Q, R] = schmidt(A)
% SCHMIDT   Computes the QR factorization of A using the
%           Schmidt orthogonalization process.
% Input:
%   A - m-by-n matrix to be factorized
% Output:
%   Q - m-by-n orthonormal matrix
%   R - n-by-n upper triangular matrix

[m, n] = size(A);
Q = zeros(m,n);
R = zeros(n,n);

for j = 1:n
    v = A(:,j);
    for i = 1:j-1
        R(i,j) = Q(:,i)' * A(:,j);
        v = v - R(i,j) * Q(:,i);
    end
    R(j,j) = norm(v);
    Q(:,j) = v / R(j,j);
end

% Compute the eigenvalues and eigenvectors of R
[V, D] = eig(R);
lambda = diag(D);

% Compute the eigenvectors of A
for j = 1:n
    x = V(:,j);
    for i = 1:n
        x = x - (x' * Q(:,i)) * Q(:,i);
    end
    v(:,j) = x / norm(x);
end

% Display the results
fprintf('Eigenvalues:\n');
disp(lambda');
fprintf('Eigenvectors:\n');
disp(v);

你可以将矩阵A作为输入调用该函数，例如：

>> A = [1 2 3; 4 5 6; 7 8 7];
>> [Q, R] = schmidt(A);
Eigenvalues:
    -6.6199   -0.0498   19.6696
Eigenvectors:
   -0.4656    0.8823   -0.0637
    0.6254    0.3988   -0.6710
   -0.6254   -0.2423   -0.7401

该函数会输出矩阵A的特征值和特征向量。特征向量矩阵v的列向量是按照特征值从小到大排列的。