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Thread Subject:
calculate eigen value in term of symbols

Subject: calculate eigen value in term of symbols

From: amit sharma

Date: 1 Dec, 2010 11:23:40

Message: 1 of 3

Dear freiend,

I have a matrix like

R =
[0 -w1 -1 0 0 0 eps;
w1 a 0 0 0 0 0;
z1 0 (x1-c) 0 0 0 0;
0 0 0 0 -w2 -1 eps;
0 0 0 w2 a 0 0;
0 0 0 z2 0 (x2-c) 0;
-0.5*eps 0 0 -0.5*eps 0 0 -1];


I want to calculate the eigenvalue in term of symbols

but i get error like

??? Error using ==> mupadfeval at 28
Error: unable to define matrix over Dom::ExpressionField()
[(Dom::Matrix(Dom::ExpressionField()))::new]

Error in ==> sym.eig at 57
        eigvals = mupadfeval('mleigenvalues',A);

Error in ==> amit11210 at 24
Q = eig(R);

i can't understant the meaning ogf this error

Plz help me

Waiting for response

Subject: calculate eigen value in term of symbols

From: Torsten Hennig

Date: 1 Dec, 2010 11:43:06

Message: 2 of 3

> Dear freiend,
>
> I have a matrix like
>
> R =
> [0 -w1 -1 0 0 0 eps;
> w1 a 0 0 0 0 0;
> z1 0 (x1-c) 0 0 0 0;
> 0 0 0 0 -w2 -1 eps;
> 0 0 0 w2 a 0 0;
> 0 0 0 z2 0 (x2-c) 0;
> -0.5*eps 0 0 -0.5*eps 0 0 -1];
>
>
> I want to calculate the eigenvalue in term of symbols
>

Besides possible technical errors in your
MATLAB code, this seems impossible
since you had to calculate an analytical expression
for the zeros of a polynomial of degree 7, whereas
such expressions only exist for polynomials of
degree <= 4.

> but i get error like
>
> ??? Error using ==> mupadfeval at 28
> Error: unable to define matrix over
> Dom::ExpressionField()
> [(Dom::Matrix(Dom::ExpressionField()))::new]
>
> Error in ==> sym.eig at 57
> eigvals = mupadfeval('mleigenvalues',A);
>
> Error in ==> amit11210 at 24
> Q = eig(R);
>
> i can't understant the meaning ogf this error
>
> Plz help me
>
> Waiting for response

Best wishes
Torsten.

Subject: calculate eigen value in term of symbols

From: Steven_Lord

Date: 1 Dec, 2010 15:04:18

Message: 3 of 3



"Torsten Hennig" <Torsten.Hennig@umsicht.fhg.de> wrote in message
news:333668001.34402.1291203816369.JavaMail.root@gallium.mathforum.org...
>> Dear freiend,
>>
>> I have a matrix like
>>
>> R =
>> [0 -w1 -1 0 0 0 eps;
>> w1 a 0 0 0 0 0;
>> z1 0 (x1-c) 0 0 0 0;
>> 0 0 0 0 -w2 -1 eps;
>> 0 0 0 w2 a 0 0;
>> 0 0 0 z2 0 (x2-c) 0;
>> -0.5*eps 0 0 -0.5*eps 0 0 -1];
>>
>>
>> I want to calculate the eigenvalue in term of symbols
>>
>
> Besides possible technical errors in your
> MATLAB code, this seems impossible
> since you had to calculate an analytical expression
> for the zeros of a polynomial of degree 7, whereas
> such expressions only exist for polynomials of
> degree <= 4.

Be careful -- there's no GENERAL solution in radicals to a polynomial of
degree greater than 4. That doesn't necessarily mean that there is no
SPECIFIC solution in radicals to a _particular_ polynomial of higher degree.

http://en.wikipedia.org/wiki/Abel%E2%80%93Ruffini_theorem

But I agree with Torsten that it's highly unlikely you're going to get a
general solution in terms of the seven symbolic variables in your matrix.
Instead I would substitute values into the matrix for those variables and
solve the problem numerically. That will likely be MUCH faster as well.

--
Steve Lord
slord@mathworks.com
To contact Technical Support use the Contact Us link on
http://www.mathworks.com

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