WOLFRAM SYSTEM MODELER

eigenValueMatrix

Return real valued block diagonal matrix J of eigenvalues of matrix A (A=V*J*Vinv)

Wolfram Language

In[1]:=
`SystemModel["Modelica.Math.Matrices.eigenValueMatrix"]`
Out[1]:=

Information

This information is part of the Modelica Standard Library maintained by the Modelica Association.

Syntax

```Matrices.eigenValueMatrix(eigenvalues);
```

Description

The function call returns a block diagonal matrix J from the two-column matrix `eigenvalues` (computed by function Matrices.eigenValues). Matrix `eigenvalues` must have the real part of the eigenvalues in the first column and the imaginary part in the second column. If an eigenvalue i has a vanishing imaginary part, then J[i,i] = eigenvalues[i,1], i.e., the diagonal element of J is the real eigenvalue. Otherwise, eigenvalue i and conjugate complex eigenvalue i+1 are used to construct a 2 by 2 diagonal block of J:

```J[i  , i]   := eigenvalues[i,1];
J[i  , i+1] := eigenvalues[i,2];
J[i+1, i]   := eigenvalues[i+1,2];
J[i+1, i+1] := eigenvalues[i+1,1];
```

Matrices.eigenValues

Syntax

J = eigenValueMatrix(eigenValues)

Inputs (1)

eigenValues Type: Real[:,2] Description: Eigen values from function eigenValues(..) (Re: first column, Im: second column)

Outputs (1)

J Type: Real[size(eigenValues, 1),size(eigenValues, 1)] Description: Real valued block diagonal matrix with eigen values (Re: 1x1 block, Im: 2x2 block)