Thread Subject:

Matrix Minimal Polynomial

Hi.
I would like to know, how could I find the minimal polynomial of a given matrix. If someone could post here a code in matlab, it would be really appreciated. Thank you.

"Norbert" wrote in message <is2omp$g31$1@newscl01ah.mathworks.com>...
> Hi.
> I would like to know, how could I find the minimal polynomial of a given matrix. If someone could post here a code in matlab, it would be really appreciated. Thank you.
- - - - - - - - -
  Look at this site:

 http://www.mathworks.com/help/toolbox/mupad/linalg/minpoly.html

Roger Stafford

"Roger Stafford" wrote in message <is43mu$ph5$1@newscl01ah.mathworks.com>...
> "Norbert" wrote in message <is2omp$g31$1@newscl01ah.mathworks.com>...
> > Hi.
> > I would like to know, how could I find the minimal polynomial of a given matrix. If someone could post here a code in matlab, it would be really appreciated. Thank you.
> - - - - - - - - -
> Look at this site:
>
> http://www.mathworks.com/help/toolbox/mupad/linalg/minpoly.html
>
> Roger Stafford

Is there a way to do the same using plain MATLAB (without MuPad). I guess MuPad uses symbolic algorithms to calculate the minimum polynomial - is there a function to do the same numerically? If not, is there a way to invoke linalg::minpoly from the workspace. By the way, to the best of my knowledge, the symbolic toolbox doesn't have support for minimal polynomials.

"Roger Stafford" wrote in message <is43mu$ph5$1@newscl01ah.mathworks.com>...
> "Norbert" wrote in message <is2omp$g31$1@newscl01ah.mathworks.com>...
> > Hi.
> > I would like to know, how could I find the minimal polynomial of a given matrix. If someone could post here a code in matlab, it would be really appreciated. Thank you.
> - - - - - - - - -
> Look at this site:
>
> http://www.mathworks.com/help/toolbox/mupad/linalg/minpoly.html
>
> Roger Stafford

Is there a way to do the same using plain MATLAB (without MuPad). I guess MuPad uses symbolic algorithms to calculate the minimum polynomial - is there a function to do the same numerically? If not, is there a way to invoke linalg::minpoly from the workspace. By the way, to the best of my knowledge, the symbolic toolbox doesn't have support for minimal polynomials.

On 08.11.11 12:58, Pantelis S wrote:

> I guess MuPad uses symbolic algorithms to calculate the minimum polynomial - is there a function to do the same numerically?

I don't think so. You probably could create something starting from
polyfun's poly.m (which computes the characteristic polynomial) by
checking the kernel before adding in another multiplicity of an
Eigenvalue, but off-hand I'm not sure if that is numerically stable.

> If not, is there a way to invoke linalg::minpoly from the workspace.

feval(symengine, 'expr', feval(symengine, 'linalg::minpoly', A, 'x'))

Kind of ugly, I know.



Christopher