Exponential of a matrix

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Hi,

There are several ways to compute the exponential of a matrix. One of
these ways consists in using the spectral decomposition of the matrix,
that the HP50g can do.

As a result, why is EXP(A), where A is a matrix, not implemented? This
would be very useful, especially for systems theory.
- -- 
Merciadri Luca
See http://www.student.montefiore.ulg.ac.be/~merciadri/
- -- 

Procrastination is the thief of time.
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0
Merciadri
3/21/2011 12:10:05 PM
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On 21 Mar, 13:10, Merciadri Luca <Luca.Mercia...@student.ulg.ac.be>
wrote:
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> Hash: SHA1
>
> Hi,
>
> There are several ways to compute the exponential of a matrix. One of
> these ways consists in using the spectral decomposition of the matrix,
> that the HP50g can do.
>
> As a result, why is EXP(A), where A is a matrix, not implemented? This
> would be very useful, especially for systems theory.
> - --
> Merciadri Luca
> Seehttp://www.student.montefiore.ulg.ac.be/~merciadri/
> - --
>
> Procrastination is the thief of time.
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>
> iEYEARECAAYFAk2HQB0ACgkQM0LLzLt8MhyVhwCglF+9ofQFo2GWGaX70QuSYawZ
> K1MAnR+nKqBh/pGiWr62zOEz7zyJJkOy
> =miqb
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You can use DIAGMAP command, see HP 50g AUR http://www.hpcalc.org/details.php?id=7141
at page 3-58:

ex. [[ 1 1 ] [ 0 2 ]] 'EXP(X)' DIAGMAP --> [[ 'EXP(1)' '-
EXP(1)+EXP(2)' ][ 0 'EXP(2)' ]]

Simone Cerica
0
supergems
3/21/2011 4:37:08 PM
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supergems <simone.cerica@gmail.com> writes:

> On 21 Mar, 13:10, Merciadri Luca <Luca.Mercia...@student.ulg.ac.be>
> wrote:
>> -----BEGIN PGP SIGNED MESSAGE-----
>> Hash: SHA1
>>
>> Hi,
>>
>> There are several ways to compute the exponential of a matrix. One of
>> these ways consists in using the spectral decomposition of the matrix,
>> that the HP50g can do.
>>
>> As a result, why is EXP(A), where A is a matrix, not implemented? This
>> would be very useful, especially for systems theory.
>> - --
>> Merciadri Luca
>> Seehttp://www.student.montefiore.ulg.ac.be/~merciadri/
>> - --
>>
>> Procrastination is the thief of time.
>> -----BEGIN PGP SIGNATURE-----
>> Version: GnuPG v1.4.9 (GNU/Linux)
>> Comment: Processed by Mailcrypt 3.5.8 <http://mailcrypt.sourceforge.net/>
>>
>> iEYEARECAAYFAk2HQB0ACgkQM0LLzLt8MhyVhwCglF+9ofQFo2GWGaX70QuSYawZ
>> K1MAnR+nKqBh/pGiWr62zOEz7zyJJkOy
>> =miqb
>> -----END PGP SIGNATURE-----
>
> You can use DIAGMAP command, see HP 50g AUR http://www.hpcalc.org/details.php?id=7141
> at page 3-58:
>
> ex. [[ 1 1 ] [ 0 2 ]] 'EXP(X)' DIAGMAP --> [[ 'EXP(1)' '-
> EXP(1)+EXP(2)' ][ 0 'EXP(2)' ]]
Thanks!

- -- 
Merciadri Luca
See http://www.student.montefiore.ulg.ac.be/~merciadri/
- -- 

The nail that sticks up will be hammered down.
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0
Merciadri
3/21/2011 4:55:50 PM
When the matrix is not diagonalizable you can use this code:

\<< DUP SIZE OBJ\-> DROP2 XQ IDN
RCLVX * SWAP - INV ILAP EXPAND
\>> 'MATEXP' STO
 
[[ 3 0 0 ][ 0 2 1 ][ 0 0 2 ]] MATEXP --> [[ 'EXP(3*X)' 0 0 ][ 0 'EXP(2*X)' 'X*EXP(2*X)' ][ 0 0 'EXP(2*X)' ]]
[[ 1 -1 ][ 0 2 ]] MATEXP --> [[ 'EXP(X)' '-(EXP(2*X)-EXP(X))' ][ 0 'EXP(2*X)' ]]
0
supergems
1/7/2015 10:24:18 PM
For numerical evaluation you could try 
matexp at
http://www.hpcalc.org/hp49/math/numeric/utilgcc.zip 

quite fast, written in hpgcc2, runs on the hp50g


best regards
Gjermund
0
gjermund
2/16/2015 11:03:39 AM
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