Eigenvalues and eigenvectors of a real matrix. If A is symmetric, then A = V * D * V' where the eigenvalue matrix D is diagonal and the eigenvector matrix V is orthogonal. I.e. A = V.Multiply(D.Multiply(V.Transpose())) and V.Multiply(V.Transpose()) equals the identity matrix. If A is not symmetric, then 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, i.e. A.Multiply(V) equals V.Multiply(D). The matrix V may be badly conditioned, or even singular, so the validity of the equation A = V * D * Inverse(V) depends upon V.cond().
Eigenvalues Class Documentation
Beispiel #1
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        public MatrixValue Function(MatrixValue M)
        {
            var ev = new Eigenvalues(M as MatrixValue);
            var m = new MatrixValue(ev.RealEigenvalues.Length, 1);

            for (var i = 1; i <= ev.RealEigenvalues.Length; i++)
            {
                m[i, 1] = new ScalarValue(ev.RealEigenvalues[i - 1], ev.ImagEigenvalues[i - 1]);
            }

            return m;
        }
Beispiel #2
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 public MatrixValue Function(MatrixValue M)
 {
     var ev = new Eigenvalues(M as MatrixValue);
     return ev.GetV();
 }