Mu Analysis and Synthesis Toolbox

Calculate eigenvalues and eigenvectors of CONSTANT and VARYING matrices

Syntax

• evals = veig(matin) 
  [evecs,evals] = veig(matin) 
  [evecs,evals] = veig(matin,'nonbalance') 
  [evecs,evals] = veig(mat1,mat2)
  

Description
veig is identical to MATLAB's command eig, but works on VARYING matrices. veig solves for the eigenvalues (evals) and optionally the eigenvectors (evecs) of the input matrix matin. veig works only on square CONSTANT or VARYING matrices. Depending on the input arguments, the following operations are performed:

evals = veig(matin) returns a VARYING vector evals containing the eigenvalues of the VARYING matrix matin for each independent variable.

[evecs,evals] = veig(matin) returns the VARYING diagonal matrix evals and a square VARYING matrix evecs whose columns are the corresponding eigenvectors for each independent variable.

[evecs,evals] = veig(matin,'nobalance') is the same as the above command without performing a preliminary balancing step. Balancing a matrix, which has very small entries due to round off error, can lead to incorrect eigenvectors.

[evecs,evals] = veig(mat1,mat2) returns a VARYING diagonal matrix of generalized eigenvalues evals and the corresponding values of generalized right eigenvectors evecs associated with each independent variable. mat1 and mat2 can be CONSTANT or VARYING matrices. If either is CONSTANT, then that same matrix is used in the generalized eigenvalue solution for each independent variable. If they are both VARYING matrices, then they must have the same independent variables.

Examples
Create a 2 x 2 random VARYING matrix and find its eigenvalues.

• see(matin)
  2 rows  2 columns
  
  iv = 0.1
  0.9304   0.5269
  0.8462   0.0920
  iv = 0.4
  0.6539   0.7012
  0.4160   0.9103
  evals = veig(matin);
  see(evals)
  2 rows1 column
  
  iv = 0.1
    1.2996
   -0.2772
  
  iv = 0.4
   0.2270
   1.3372
  

• mat1 = matin; 
  mat2 = vpck([4*eye(2);3*eye(2)],[.1 .4]); 
  [evecs,evals] = veig(mat1,mat2);
  see(evecs)
  2 rows  2 columns
  
  iv = 0.1
   0.8190   -0.3999
   0.5738    0.9166
  
  iv = 0.4
   0.8542   0.7162
  -0.5200   0.6979
  see(evals)
  2 rows   2 columns
  
  iv = 0.1
   0.3249   0
   0       -0.0693
  iv = 0.4
   0.0757   0
   0        0.4457
  
  

Algorithm
veig calls the MATLAB eig command.

See Also
eig, indvcmp, svd, vsvd, vpoly, vroots

vebe

veval