Solve symbolic Sylvester-like equation in MATLAB or MAPLEDifferentiation of a parametric function using MATLAB or MapleSolving symbolic linear equations with mapleTurning Matrix Equation into a Sylvester EquationSolving integral equation in matlabSolve intregal equation using MATLABWorking with Maple toolbox for MatlabSolving a Sylvester equation - Won't give me the right answer in MATLABNonlinear Sylvester-like equationEquation of two Matlab function filesUsing MATLAB to solve Poisson matrix equation
Brexit - No Deal Rejection
A Cautionary Suggestion
Is a party consisting of only a bard, a cleric, and a warlock functional long-term?
Are all passive ability checks floors for active ability checks?
Can a druid choose the size of its wild shape beast?
Why doesn't the EU now just force the UK to choose between referendum and no-deal?
compactness of a set where am I going wrong
How Could an Airship Be Repaired Mid-Flight
Is it true that good novels will automatically sell themselves on Amazon (and so on) and there is no need for one to waste time promoting?
SOQL: Populate a Literal List in WHERE IN Clause
PTIJ: Who should I vote for? (21st Knesset Edition)
How to read the value of this capacitor?
Does Mathematica reuse previous computations?
Why one should not leave fingerprints on bulbs and plugs?
How to explain that I do not want to visit a country due to personal safety concern?
If I can solve Sudoku can I solve Travelling Salesman Problem(TSP)? If yes, how?
Employee lack of ownership
Gravity magic - How does it work?
Most cost effective thermostat setting: consistent temperature vs. lowest temperature possible
Who is flying the vertibirds?
How do I hide Chekhov's Gun?
What did Alexander Pope mean by "Expletives their feeble Aid do join"?
Interplanetary conflict, some disease destroys the ability to understand or appreciate music
How difficult is it to simply disable/disengage the MCAS on Boeing 737 Max 8 & 9 Aircraft?
Solve symbolic Sylvester-like equation in MATLAB or MAPLE
Differentiation of a parametric function using MATLAB or MapleSolving symbolic linear equations with mapleTurning Matrix Equation into a Sylvester EquationSolving integral equation in matlabSolve intregal equation using MATLABWorking with Maple toolbox for MatlabSolving a Sylvester equation - Won't give me the right answer in MATLABNonlinear Sylvester-like equationEquation of two Matlab function filesUsing MATLAB to solve Poisson matrix equation
$begingroup$
I'm looking for a way to solve a symbolic Sylvester-like equation in MATLAB or MAPLE (or any other available tool). In particular, I have the following equation,
$$AX+XA=B$$
where, $A$ has some parameters in it, e.g.,
$$A=beginbmatrixa+1 & 2\3 & 1endbmatrix$$
$B$ is known and I want to solve for $X$ as a function of $a$.
matrix-equations matlab maple sylvester-equation
edited Mar 11 at 21:44
Rodrigo de Azevedo
13k41960
asked Mar 11 at 21:09
MohammadMohammad
206
$endgroup$
|
show 1 more comment
$begingroup$
I'm looking for a way to solve a symbolic Sylvester-like equation in MATLAB or MAPLE (or any other available tool). In particular, I have the following equation,
$$AX+XA=B$$
where, $A$ has some parameters in it, e.g.,
$$A=beginbmatrixa+1 & 2\3 & 1endbmatrix$$
$B$ is known and I want to solve for $X$ as a function of $a$.
matrix-equations matlab maple sylvester-equation
edited Mar 11 at 21:44
Rodrigo de Azevedo
13k41960
asked Mar 11 at 21:09
MohammadMohammad
206
$endgroup$
$begingroup$
Matlab has now a "sylvester" function uk.mathworks.com/help/matlab/ref/sylvester.html
$endgroup$
– Jean Marie
Mar 11 at 21:41
$begingroup$
Why not use vectorization?
$endgroup$
– Rodrigo de Azevedo
Mar 11 at 21:45
$begingroup$
@JeanMarie Yes, but the input arguments must be numeric arrays.
$endgroup$
– Mohammad
Mar 11 at 21:46
$begingroup$
@RodrigodeAzevedo Can you please describe more?
$endgroup$
– Mohammad
Mar 11 at 21:46
$begingroup$
Vectorization converts the matrix equation into a system of $4$ linear equations in $4$ unknowns, which is easy to solve symbolically. In MATLAB, usekronfor the Kronecker product andreshapefor the vectorization and un-vectorization.
$endgroup$
– Rodrigo de Azevedo
Mar 11 at 21:48
|
show 1 more comment
$begingroup$
I'm looking for a way to solve a symbolic Sylvester-like equation in MATLAB or MAPLE (or any other available tool). In particular, I have the following equation,
$$AX+XA=B$$
where, $A$ has some parameters in it, e.g.,
$$A=beginbmatrixa+1 & 2\3 & 1endbmatrix$$
$B$ is known and I want to solve for $X$ as a function of $a$.
matrix-equations matlab maple sylvester-equation
edited Mar 11 at 21:44
Rodrigo de Azevedo
13k41960
asked Mar 11 at 21:09
MohammadMohammad
206
$endgroup$
I'm looking for a way to solve a symbolic Sylvester-like equation in MATLAB or MAPLE (or any other available tool). In particular, I have the following equation,
$$AX+XA=B$$
where, $A$ has some parameters in it, e.g.,
$$A=beginbmatrixa+1 & 2\3 & 1endbmatrix$$
$B$ is known and I want to solve for $X$ as a function of $a$.
matrix-equations matlab maple sylvester-equation
matrix-equations matlab maple sylvester-equation
edited Mar 11 at 21:44
Rodrigo de Azevedo
13k41960
asked Mar 11 at 21:09
MohammadMohammad
206
edited Mar 11 at 21:44
Rodrigo de Azevedo
13k41960
asked Mar 11 at 21:09
MohammadMohammad
206
edited Mar 11 at 21:44
Rodrigo de Azevedo
13k41960
edited Mar 11 at 21:44
Rodrigo de Azevedo
13k41960
edited Mar 11 at 21:44
Rodrigo de Azevedo
13k41960
13k41960
asked Mar 11 at 21:09
MohammadMohammad
206
asked Mar 11 at 21:09
MohammadMohammad
206
asked Mar 11 at 21:09
MohammadMohammad
206
206
$begingroup$
Matlab has now a "sylvester" function uk.mathworks.com/help/matlab/ref/sylvester.html
$endgroup$
– Jean Marie
Mar 11 at 21:41
$begingroup$
Why not use vectorization?
$endgroup$
– Rodrigo de Azevedo
Mar 11 at 21:45
$begingroup$
@JeanMarie Yes, but the input arguments must be numeric arrays.
$endgroup$
– Mohammad
Mar 11 at 21:46
$begingroup$
@RodrigodeAzevedo Can you please describe more?
$endgroup$
– Mohammad
Mar 11 at 21:46
$begingroup$
Vectorization converts the matrix equation into a system of $4$ linear equations in $4$ unknowns, which is easy to solve symbolically. In MATLAB, usekronfor the Kronecker product andreshapefor the vectorization and un-vectorization.
$endgroup$
– Rodrigo de Azevedo
Mar 11 at 21:48
|
show 1 more comment
$begingroup$
Matlab has now a "sylvester" function uk.mathworks.com/help/matlab/ref/sylvester.html
$endgroup$
– Jean Marie
Mar 11 at 21:41
$begingroup$
Why not use vectorization?
$endgroup$
– Rodrigo de Azevedo
Mar 11 at 21:45
$begingroup$
@JeanMarie Yes, but the input arguments must be numeric arrays.
$endgroup$
– Mohammad
Mar 11 at 21:46
$begingroup$
@RodrigodeAzevedo Can you please describe more?
$endgroup$
– Mohammad
Mar 11 at 21:46
$begingroup$
Vectorization converts the matrix equation into a system of $4$ linear equations in $4$ unknowns, which is easy to solve symbolically. In MATLAB, usekronfor the Kronecker product andreshapefor the vectorization and un-vectorization.
$endgroup$
– Rodrigo de Azevedo
Mar 11 at 21:48
$begingroup$
Matlab has now a "sylvester" function uk.mathworks.com/help/matlab/ref/sylvester.html
$endgroup$
– Jean Marie
Mar 11 at 21:41
$begingroup$
Matlab has now a "sylvester" function uk.mathworks.com/help/matlab/ref/sylvester.html
$endgroup$
– Jean Marie
Mar 11 at 21:41
$begingroup$
Why not use vectorization?
$endgroup$
– Rodrigo de Azevedo
Mar 11 at 21:45
$begingroup$
Why not use vectorization?
$endgroup$
– Rodrigo de Azevedo
Mar 11 at 21:45
$begingroup$
@JeanMarie Yes, but the input arguments must be numeric arrays.
$endgroup$
– Mohammad
Mar 11 at 21:46
$begingroup$
@JeanMarie Yes, but the input arguments must be numeric arrays.
$endgroup$
– Mohammad
Mar 11 at 21:46
$begingroup$
@RodrigodeAzevedo Can you please describe more?
$endgroup$
– Mohammad
Mar 11 at 21:46
$begingroup$
@RodrigodeAzevedo Can you please describe more?
$endgroup$
– Mohammad
Mar 11 at 21:46
$begingroup$
Vectorization converts the matrix equation into a system of $4$ linear equations in $4$ unknowns, which is easy to solve symbolically. In MATLAB, use
kron for the Kronecker product and reshape for the vectorization and un-vectorization.$endgroup$
– Rodrigo de Azevedo
Mar 11 at 21:48
$begingroup$
Vectorization converts the matrix equation into a system of $4$ linear equations in $4$ unknowns, which is easy to solve symbolically. In MATLAB, use
kron for the Kronecker product and reshape for the vectorization and un-vectorization.$endgroup$
– Rodrigo de Azevedo
Mar 11 at 21:48
|
show 1 more comment
1 Answer
1
active
oldest
votes
$begingroup$
You could write the Sylvester equation as a linear system:
beginequation
(I_2 otimes A + A^T otimes I_2) mathrmvec X = mathrmvec B
endequation
which you can then solve for $mathrmvecX$:
beginalign
mathrmvecX
& = (I_2 otimes A + A^T otimes I_2)^-1 mathrmvec B \
& = fracmathrmadj (I_2 otimes A + A^T otimes I_2)mathrmdet (I_2 otimes A + A^T otimes I_2) mathrmvec B
endalign
and finally reshape back to a 2 by 2 matrix.
answered Mar 11 at 21:50
Koen TielsKoen Tiels
1706
$endgroup$
add a comment |
Your Answer
StackExchange.ifUsing("editor", function ()
return StackExchange.using("mathjaxEditing", function ()
StackExchange.MarkdownEditor.creationCallbacks.add(function (editor, postfix)
StackExchange.mathjaxEditing.prepareWmdForMathJax(editor, postfix, [["$", "$"], ["\\(","\\)"]]);
);
);
, "mathjax-editing");
StackExchange.ready(function()
var channelOptions =
tags: "".split(" "),
id: "69"
;
initTagRenderer("".split(" "), "".split(" "), channelOptions);
StackExchange.using("externalEditor", function()
// Have to fire editor after snippets, if snippets enabled
if (StackExchange.settings.snippets.snippetsEnabled)
StackExchange.using("snippets", function()
createEditor();
);
else
createEditor();
);
function createEditor()
StackExchange.prepareEditor(
heartbeatType: 'answer',
autoActivateHeartbeat: false,
convertImagesToLinks: true,
noModals: true,
showLowRepImageUploadWarning: true,
reputationToPostImages: 10,
bindNavPrevention: true,
postfix: "",
imageUploader:
brandingHtml: "Powered by u003ca class="icon-imgur-white" href="https://imgur.com/"u003eu003c/au003e",
contentPolicyHtml: "User contributions licensed under u003ca href="https://creativecommons.org/licenses/by-sa/3.0/"u003ecc by-sa 3.0 with attribution requiredu003c/au003e u003ca href="https://stackoverflow.com/legal/content-policy"u003e(content policy)u003c/au003e",
allowUrls: true
,
noCode: true, onDemand: true,
discardSelector: ".discard-answer"
,immediatelyShowMarkdownHelp:true
);
);
Sign up or log in
StackExchange.ready(function ()
StackExchange.helpers.onClickDraftSave('#login-link');
);
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
StackExchange.ready(
function ()
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmath.stackexchange.com%2fquestions%2f3144254%2fsolve-symbolic-sylvester-like-equation-in-matlab-or-maple%23new-answer', 'question_page');
);
Post as a guest
Required, but never shown
1 Answer
1
active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
$begingroup$
You could write the Sylvester equation as a linear system:
beginequation
(I_2 otimes A + A^T otimes I_2) mathrmvec X = mathrmvec B
endequation
which you can then solve for $mathrmvecX$:
beginalign
mathrmvecX
& = (I_2 otimes A + A^T otimes I_2)^-1 mathrmvec B \
& = fracmathrmadj (I_2 otimes A + A^T otimes I_2)mathrmdet (I_2 otimes A + A^T otimes I_2) mathrmvec B
endalign
and finally reshape back to a 2 by 2 matrix.
answered Mar 11 at 21:50
Koen TielsKoen Tiels
1706
$endgroup$
add a comment |
$begingroup$
You could write the Sylvester equation as a linear system:
beginequation
(I_2 otimes A + A^T otimes I_2) mathrmvec X = mathrmvec B
endequation
which you can then solve for $mathrmvecX$:
beginalign
mathrmvecX
& = (I_2 otimes A + A^T otimes I_2)^-1 mathrmvec B \
& = fracmathrmadj (I_2 otimes A + A^T otimes I_2)mathrmdet (I_2 otimes A + A^T otimes I_2) mathrmvec B
endalign
and finally reshape back to a 2 by 2 matrix.
answered Mar 11 at 21:50
Koen TielsKoen Tiels
1706
$endgroup$
add a comment |
$begingroup$
You could write the Sylvester equation as a linear system:
beginequation
(I_2 otimes A + A^T otimes I_2) mathrmvec X = mathrmvec B
endequation
which you can then solve for $mathrmvecX$:
beginalign
mathrmvecX
& = (I_2 otimes A + A^T otimes I_2)^-1 mathrmvec B \
& = fracmathrmadj (I_2 otimes A + A^T otimes I_2)mathrmdet (I_2 otimes A + A^T otimes I_2) mathrmvec B
endalign
and finally reshape back to a 2 by 2 matrix.
answered Mar 11 at 21:50
Koen TielsKoen Tiels
1706
$endgroup$
You could write the Sylvester equation as a linear system:
beginequation
(I_2 otimes A + A^T otimes I_2) mathrmvec X = mathrmvec B
endequation
which you can then solve for $mathrmvecX$:
beginalign
mathrmvecX
& = (I_2 otimes A + A^T otimes I_2)^-1 mathrmvec B \
& = fracmathrmadj (I_2 otimes A + A^T otimes I_2)mathrmdet (I_2 otimes A + A^T otimes I_2) mathrmvec B
endalign
and finally reshape back to a 2 by 2 matrix.
answered Mar 11 at 21:50
Koen TielsKoen Tiels
1706
edited Mar 12 at 21:49
answered Mar 11 at 21:50
Koen TielsKoen Tiels
1706
answered Mar 11 at 21:50
Koen TielsKoen Tiels
1706
answered Mar 11 at 21:50
Koen TielsKoen Tiels
1706
1706
add a comment |
add a comment |
Thanks for contributing an answer to Mathematics Stack Exchange!
- Please be sure to answer the question. Provide details and share your research!
But avoid …
- Asking for help, clarification, or responding to other answers.
- Making statements based on opinion; back them up with references or personal experience.
Use MathJax to format equations. MathJax reference.
To learn more, see our tips on writing great answers.
Sign up or log in
StackExchange.ready(function ()
StackExchange.helpers.onClickDraftSave('#login-link');
);
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
StackExchange.ready(
function ()
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmath.stackexchange.com%2fquestions%2f3144254%2fsolve-symbolic-sylvester-like-equation-in-matlab-or-maple%23new-answer', 'question_page');
);
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function ()
StackExchange.helpers.onClickDraftSave('#login-link');
);
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function ()
StackExchange.helpers.onClickDraftSave('#login-link');
);
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function ()
StackExchange.helpers.onClickDraftSave('#login-link');
);
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
$begingroup$
Matlab has now a "sylvester" function uk.mathworks.com/help/matlab/ref/sylvester.html
$endgroup$
– Jean Marie
Mar 11 at 21:41
$begingroup$
Why not use vectorization?
$endgroup$
– Rodrigo de Azevedo
Mar 11 at 21:45
$begingroup$
@JeanMarie Yes, but the input arguments must be numeric arrays.
$endgroup$
– Mohammad
Mar 11 at 21:46
$begingroup$
@RodrigodeAzevedo Can you please describe more?
$endgroup$
– Mohammad
Mar 11 at 21:46
$begingroup$
Vectorization converts the matrix equation into a system of $4$ linear equations in $4$ unknowns, which is easy to solve symbolically. In MATLAB, use
kronfor the Kronecker product andreshapefor the vectorization and un-vectorization.$endgroup$
– Rodrigo de Azevedo
Mar 11 at 21:48