Mu Analysis and Synthesis Toolbox

Find coefficients and roots of a characteristic polynomial from a CONSTANT or VARYING matrix

Syntax

• matout = vpoly(matin) 
  vecout = vpoly(vecin) 
  vecout = vroots(vecin)
  

Description
vpoly forms an n + 1 element VARYING row vector whose elements form the coefficients of the characteristic polynomial, det(sI - matin(i)), if matin is an
n x n VARYING matrix. The coefficients are ordered in descending powers of s. If the input is a column vector vecin containing the roots of a polynomial, vpoly(vecin) returns a VARYING row vector whose elements are the coefficients of the corresponding characteristic polynomial.

vroots returns as a VARYING column vector vecout whose elements are the roots of the polynomial at each independent variable, if vecin is a VARYING row vector containing the coefficients of a polynomial. vpoly and vroots are identical to the MATLAB poly and roots commands, but also work on VARYING matrices.

Examples
Given a 3 x 3 VARYING matrix, find the characteristic polynomial and its roots. Compare this to finding the eigenvalues of the input matrix via veig.

• see(matin)
  3 rows      3 columns
  iv = 0.1
  1   2   3
  4   5   6
  7   8   9
  iv = 0.4
  10   11   12
  13   14   15
  16   17   18
  matout = vpoly(matin);
  see(matout)
  1 row      4 columns
  iv = 0.1
  l.0000e+00    -1.5000e+01    -1.8000e+01    -1.4483e-14
  iv = 0.4
  l.0000e+00    -4.2000e+01    -1.8000e+01     1.2818e-14
  vecout = vroots(matout);
  see(vecout)
  3 rows       1 column
  iv = 0.1
   1.6117e+01
  -1.1168e+00
  -8.0463e-16
  
  iv = 0.4
   4.2424e+01
  -4.2429e-01
  7.1212e-16
  evals = veig(matin);
  see(evals)
  3 rows        1 column
  
  iv = 0.1
   1.6117e+01
  -1.1168e+00
  -8.0463e-16
  iv = 0.4
   4.2424e+01
  -4.2429e-01
   7.1212e-16
  

Algorithm
vpoly and vroots call the MATLAB poly and roots commands.

See Also
eig, poly, roots, veig

vplot

vsvd, vrho, vschur