Returns the eigenvectors.
A double matrix containing the eigenvectors of the matrix from which the factors were extracted.
The j-th column of the eigenvector matrix corresponds to the j-th eigenvalue. The eigenvectors are normalized to each have Euclidean length equal to one. Also, the sign of each vector is set so that the largest component in magnitude (the first of the largest if there are ties) is made positive. Note that the eigenvectors are usually not the eigenvectors of the input matrix cov. They are the eigenvectors of the input matrix cov when the Principal Component method is used.
| Exception Type | Condition |
|---|---|
| RankException | is thrown if the rank of the covariance matrix is less than the number of factors. |
| NoDegreesOfFreedomException | is thrown if there are no degrees of freedom for the significance testing. |
| NotSemiDefiniteException | is thrown if the Hessian matrix not semi-definite. |
| NotPositiveSemiDefiniteException | is thrown if the covariance matrix is not positive semi-definite. |
| NotPositiveDefiniteException | is thrown if the covariance matrix is not positive definite because a variable is linearly releated to other variables. |
| SingularException | is thrown if the covariance matrix is singular. |
| BadVarianceException | is thrown if the input variance is not in the allowed range. |
| EigenvalueException | is thrown if an error occured in calculating the eigenvalues of the adjusted (inverse) covariance matrix. Check the input covariance matrix. |
| NonPositiveEigenvalueException | is thrown if in alpha factor analysis an eigenvalue is not positive. As all eigenvalues corresponding to the factors must be positive, either the number of factors must be reduced, or new initial estimates for the unique variances must be given. |
FactorAnalysis Class | Imsl.Stat Namespace