Determines the eigenvalues and eigenvectors of a real square matrix.

In the mathematical discipline of linear algebra, eigendecomposition or sometimes spectral decomposition is the factorization of a matrix into a canonical form, whereby the matrix is represented in terms of its eigenvalues and eigenvectors.

If A is symmetric, then A = V * D * V' and A = V * V' where the eigenvalue matrix D is diagonal and the eigenvector matrix V is orthogonal. If A is not symmetric, the eigenvalue matrix D is block diagonal with the real eigenvalues in 1-by-1 blocks and any complex eigenvalues, lambda + i*mu, in 2-by-2 blocks, [lambda, mu; -mu, lambda]. The columns of V represent the eigenvectors in the sense that A * V = V * D. The matrix V may be badly conditioned, or even singular, so the validity of the equation A = V * D * inverse(V) depends upon the condition of V.

Inheritance: ICloneable
EigenvalueDecompositionF Class Documentation
Example #1
0
        /// <summary>
        ///   Creates a new object that is a copy of the current instance.
        /// </summary>
        /// <returns>
        ///   A new object that is a copy of this instance.
        /// </returns>
        public object Clone()
        {
            var clone = new EigenvalueDecompositionF();

            clone.d         = (Single[])d.Clone();
            clone.e         = (Single[])e.Clone();
            clone.H         = (Single[, ])H.Clone();
            clone.n         = n;
            clone.ort       = (Single[])ort;
            clone.symmetric = symmetric;
            clone.V         = (Single[, ])V.Clone();
            return(clone);
        }
Example #2
0
 /// <summary>
 ///   Creates a new object that is a copy of the current instance.
 /// </summary>
 /// <returns>
 ///   A new object that is a copy of this instance.
 /// </returns>
 public object Clone()
 {
     var clone = new EigenvalueDecompositionF();
     clone.d = (Single[])d.Clone();
     clone.e = (Single[])e.Clone();
     clone.H = (Single[,])H.Clone();
     clone.n = n;
     clone.ort = (Single[])ort;
     clone.symmetric = symmetric;
     clone.V = (Single[,])V.Clone();
     return clone;
 }