我正在尝试为下面的矩阵计算特征向量和特征值。我能够得到结果，但所有特征向量都是正的
示例：
12.48 -1.88 -6.7
-1.88 26.7 4.32
-6.7 4.32 21.2
[1] Real Eigenvalue = 8.8362 = S3
[1] Real Eigenvector：
0.8753
-0.0247
0.4830
[2] Real Eigenvalue = 20.9867 = S2
[2] Real Eigenvector：
0.3873
0.6337
-0.6696
[3] Real Eigenvalue = 30.5570 = S1
[3] Real Eigenvector：
0.2895
-0.7731
-0.5643
以下是我测试时的方法和输出。
/**
* Computes the Principal eigenvalues of a given matrix
*
* @param matrix matrix in which eigenvalues are computed
* @return Principal eigenvalues list in an ascending order
*/
public List<Double> getPrincipalEigenValues(DoubleMatrix matrix) {
List<Double> EigenValuesList = new ArrayList<Double>();// initialize a list to store eigenvalues
ComplexDoubleMatrix eigenvalues = Eigen.eigenvalues(matrix);// compute eigenvalues
for (ComplexDouble eigenvalue : eigenvalues.toArray()) {
Double value = Double.parseDouble(String.format("%.2f ", eigenvalue.abs()));
EigenValuesList.add(value);
}
//it returns Principal Eigen Values in the order of [S3, S2, S1]
return EigenValuesList;
}
/**
* Computes the Principal eigenvectors of a given matrix
*
* @param matrix matrix in which eigenvectors are computed
* @return Principal eigenvectors list in the same order as the eigenvalues
*/
public List<Double> getPrincipalEigenVectors(DoubleMatrix matrix) {
List<Double> EigenVectorList = new ArrayList<Double>();// initialize a list to store veigenvectors
ComplexDoubleMatrix eigenvectors = Eigen.eigenvectors(matrix)[0];// compute veigenvectors
for (ComplexDouble eigenvector : eigenvectors.toArray()) {
Double value = Double.parseDouble(String.format("%.4f ", eigenvector.abs()));
EigenVectorList.add(value);
}
//it returns Principal Eigen Vectors in the order of [n3x, n3y, n3z,n2x, n2y, n2z,n1x, n1y, n1z]
return EigenVectorList;
}
测试方法后的结果。
主要特征值[8.84,20.99,30.56] Principal EigenVectors [0.8753,0.0247,0.483,0.3873,0.6337,0.6666,0.2895,0.7771,0.5643]