我最近在用C++中有个Eigen库来求解矩阵的特征值和特征向量来对标Matlab求出的结果,结果发现C++Eigen求出来的特征向量和Matlab中eig函数求出来的特征向量符号相反,请问这是为什么?
附代码结果
M是特征向量,N是特征值
C++代码
#include <cmath>
#include <iostream>
#include <stdlib.h>
#include<ctime>
#include<Eigen/Dense>
#include<Eigen/Eigenvalues>
using namespace std;
using namespace Eigen;
int main()
{
MatrixXd Q(3,3);
Q << 1, 2, 3, 2,5,6,3,6,9;
cout << "Q" << endl << Q << endl;
EigenSolver<MatrixXd> es(Q);
MatrixXcd evecs = es.eigenvectors();
MatrixXd M;
M = evecs.real();
// cout << "evecs" << endl << evecs << endl;
cout << "M" << endl << M << endl;
MatrixXcd evals = es.eigenvalues();
MatrixXd D_temp,N;
D_temp = evals.real();
N = D_temp.asDiagonal();
// cout << "evals" << endl << evals << endl;
// cout << "D_temp" << endl << D_temp << endl;
cout << "N" << endl << N << endl;
MatrixXf::Index evalsMax;
M.rowwise().sum().maxCoeff(&evalsMax);
cout << "evalsMax" << endl << evalsMax << endl;
}
结果
Q
1 2 3
2 5 6
3 6 9
M
-0.261496 -0.948683 0.177819
-0.562313 -1.0723e-15 -0.826924
-0.784489 0.316228 0.533457
N
14.3007 0 0
0 -1.25844e-15 0
0 0 0.699265
Matlab代码
Q=[1,2,3;2,5,6;3,6,9]
[M,N]=eig(Q)
结果
Q =
1 2 3
2 5 6
3 6 9
M =
0.948683298050514 -0.177819105969114 0.261496396824784
0.000000000000001 0.826924213893541 0.562313386357241
-0.316227766016839 -0.533457317907340 0.784489190474354
N =
-0.000000000000000 0 0
0 0.699264745632276 0
0 0 14.300735254367723