Change of basis in Mathematica












2














I'm trying to set up a change of basis matrix from the base V -> W with the RowReduce function that's built into Mathematica. I am then supposed to verify the result by taking the product of the change of basis matrix and multiplying it with the co-ordinate vector for x. You can see the Bases and the vector x below.



So, my question is, how do I setup the change of basis matrix and then verify it, with just the RowReduce function? Thanks in advance.



V = {{1, 3}, {4, 6}}

W = {{4, 6}, {2, 5}} 



x = {6, 6}





matrix mathematical-optimization linear-algebra







share|improve this question
























  • Pleeeease. Don't use MatrixForm in computations. See here why. Moreover, it would be appreciated if you would post copyable Mathematica code instead of images.
    – Henrik Schumacher
    17 hours ago






  • 1




    @HenrikSchumacher I'll edit the post then :)
    – wznd
    17 hours ago
















2














I'm trying to set up a change of basis matrix from the base V -> W with the RowReduce function that's built into Mathematica. I am then supposed to verify the result by taking the product of the change of basis matrix and multiplying it with the co-ordinate vector for x. You can see the Bases and the vector x below.



So, my question is, how do I setup the change of basis matrix and then verify it, with just the RowReduce function? Thanks in advance.



V = {{1, 3}, {4, 6}}

W = {{4, 6}, {2, 5}} 



x = {6, 6}





matrix mathematical-optimization linear-algebra







share|improve this question
























  • Pleeeease. Don't use MatrixForm in computations. See here why. Moreover, it would be appreciated if you would post copyable Mathematica code instead of images.
    – Henrik Schumacher
    17 hours ago






  • 1




    @HenrikSchumacher I'll edit the post then :)
    – wznd
    17 hours ago














2












2








2







I'm trying to set up a change of basis matrix from the base V -> W with the RowReduce function that's built into Mathematica. I am then supposed to verify the result by taking the product of the change of basis matrix and multiplying it with the co-ordinate vector for x. You can see the Bases and the vector x below.



So, my question is, how do I setup the change of basis matrix and then verify it, with just the RowReduce function? Thanks in advance.



V = {{1, 3}, {4, 6}}

W = {{4, 6}, {2, 5}} 



x = {6, 6}





matrix mathematical-optimization linear-algebra







share|improve this question















I'm trying to set up a change of basis matrix from the base V -> W with the RowReduce function that's built into Mathematica. I am then supposed to verify the result by taking the product of the change of basis matrix and multiplying it with the co-ordinate vector for x. You can see the Bases and the vector x below.



So, my question is, how do I setup the change of basis matrix and then verify it, with just the RowReduce function? Thanks in advance.



V = {{1, 3}, {4, 6}}

W = {{4, 6}, {2, 5}} 



x = {6, 6}





matrix mathematical-optimization linear-algebra




matrix mathematical-optimization linear-algebra






share|improve this question















share|improve this question













share|improve this question




share|improve this question








edited 17 hours ago

























asked 18 hours ago









wznd

315




315












  • Pleeeease. Don't use MatrixForm in computations. See here why. Moreover, it would be appreciated if you would post copyable Mathematica code instead of images.
    – Henrik Schumacher
    17 hours ago






  • 1




    @HenrikSchumacher I'll edit the post then :)
    – wznd
    17 hours ago


















  • Pleeeease. Don't use MatrixForm in computations. See here why. Moreover, it would be appreciated if you would post copyable Mathematica code instead of images.
    – Henrik Schumacher
    17 hours ago






  • 1




    @HenrikSchumacher I'll edit the post then :)
    – wznd
    17 hours ago
















Pleeeease. Don't use MatrixForm in computations. See here why. Moreover, it would be appreciated if you would post copyable Mathematica code instead of images.
– Henrik Schumacher
17 hours ago




Pleeeease. Don't use MatrixForm in computations. See here why. Moreover, it would be appreciated if you would post copyable Mathematica code instead of images.
– Henrik Schumacher
17 hours ago




1




1




@HenrikSchumacher I'll edit the post then :)
– wznd
17 hours ago




@HenrikSchumacher I'll edit the post then :)
– wznd
17 hours ago










1 Answer
1






active

oldest

votes


















4














This might give you an idea... I merge V and W into one matrix with ArrayFlatten and apply Gaussian elimination by RowReduce.



V = {{1, 3}, {4, 6}};

W = {{4, 6}, {2, 5}};

B = RowReduce[ArrayFlatten[{{V, W}}]][[All, 3 ;;]]

V.B == W



{{-3, -(7/2)}, {7/3, 19/6}}



True







share|improve this answer























  • Ah, smart. Wasn't thinking about how you could compare the two functions that easily. Just one question though. What does the ArrayFlatten, and the [[All, 3 ;;]] commands mean? Thank you very much for your answer.
    – wznd
    17 hours ago










  • ArrayFlatten can merge block matrices to a single matrix. And A[[All, 3 ;;]] reads off the columns 3 to Dimensions[A][[2]] of a matrix A. See the documentation of Part and Span for details.
    – Henrik Schumacher
    17 hours ago










  • Ah, now I get it. Thank you so much. If i were to calculate the change of basis matrix from W -> V, using the Inverse function, would I first take the inverse of W, and then multiply W^1 * V?
    – wznd
    17 hours ago










  • You're welcome. I'd rather use V.Inverse[W] or W.Inverse[V] depending on which direction you would like to have.
    – Henrik Schumacher
    17 hours ago










  • Well, I'd like to know the change of basis matrix from the base W -> V, so how would the function look like?
    – wznd
    16 hours ago











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: "387"
};
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: false,
noModals: true,
showLowRepImageUploadWarning: true,
reputationToPostImages: null,
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
},
onDemand: true,
discardSelector: ".discard-answer"
,immediatelyShowMarkdownHelp:true
});


}
});














draft saved

draft discarded


















StackExchange.ready(
function () {
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmathematica.stackexchange.com%2fquestions%2f188455%2fchange-of-basis-in-mathematica%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









4














This might give you an idea... I merge V and W into one matrix with ArrayFlatten and apply Gaussian elimination by RowReduce.



V = {{1, 3}, {4, 6}};

W = {{4, 6}, {2, 5}};

B = RowReduce[ArrayFlatten[{{V, W}}]][[All, 3 ;;]]

V.B == W



{{-3, -(7/2)}, {7/3, 19/6}}



True







share|improve this answer























  • Ah, smart. Wasn't thinking about how you could compare the two functions that easily. Just one question though. What does the ArrayFlatten, and the [[All, 3 ;;]] commands mean? Thank you very much for your answer.
    – wznd
    17 hours ago










  • ArrayFlatten can merge block matrices to a single matrix. And A[[All, 3 ;;]] reads off the columns 3 to Dimensions[A][[2]] of a matrix A. See the documentation of Part and Span for details.
    – Henrik Schumacher
    17 hours ago










  • Ah, now I get it. Thank you so much. If i were to calculate the change of basis matrix from W -> V, using the Inverse function, would I first take the inverse of W, and then multiply W^1 * V?
    – wznd
    17 hours ago










  • You're welcome. I'd rather use V.Inverse[W] or W.Inverse[V] depending on which direction you would like to have.
    – Henrik Schumacher
    17 hours ago










  • Well, I'd like to know the change of basis matrix from the base W -> V, so how would the function look like?
    – wznd
    16 hours ago
















4














This might give you an idea... I merge V and W into one matrix with ArrayFlatten and apply Gaussian elimination by RowReduce.



V = {{1, 3}, {4, 6}};

W = {{4, 6}, {2, 5}};

B = RowReduce[ArrayFlatten[{{V, W}}]][[All, 3 ;;]]

V.B == W



{{-3, -(7/2)}, {7/3, 19/6}}



True







share|improve this answer























  • Ah, smart. Wasn't thinking about how you could compare the two functions that easily. Just one question though. What does the ArrayFlatten, and the [[All, 3 ;;]] commands mean? Thank you very much for your answer.
    – wznd
    17 hours ago










  • ArrayFlatten can merge block matrices to a single matrix. And A[[All, 3 ;;]] reads off the columns 3 to Dimensions[A][[2]] of a matrix A. See the documentation of Part and Span for details.
    – Henrik Schumacher
    17 hours ago










  • Ah, now I get it. Thank you so much. If i were to calculate the change of basis matrix from W -> V, using the Inverse function, would I first take the inverse of W, and then multiply W^1 * V?
    – wznd
    17 hours ago










  • You're welcome. I'd rather use V.Inverse[W] or W.Inverse[V] depending on which direction you would like to have.
    – Henrik Schumacher
    17 hours ago










  • Well, I'd like to know the change of basis matrix from the base W -> V, so how would the function look like?
    – wznd
    16 hours ago














4












4








4






This might give you an idea... I merge V and W into one matrix with ArrayFlatten and apply Gaussian elimination by RowReduce.



V = {{1, 3}, {4, 6}};

W = {{4, 6}, {2, 5}};

B = RowReduce[ArrayFlatten[{{V, W}}]][[All, 3 ;;]]

V.B == W



{{-3, -(7/2)}, {7/3, 19/6}}



True







share|improve this answer














This might give you an idea... I merge V and W into one matrix with ArrayFlatten and apply Gaussian elimination by RowReduce.



V = {{1, 3}, {4, 6}};

W = {{4, 6}, {2, 5}};

B = RowReduce[ArrayFlatten[{{V, W}}]][[All, 3 ;;]]

V.B == W



{{-3, -(7/2)}, {7/3, 19/6}}



True








share|improve this answer














share|improve this answer



share|improve this answer








edited 17 hours ago

























answered 17 hours ago









Henrik Schumacher

48.6k467137




48.6k467137












  • Ah, smart. Wasn't thinking about how you could compare the two functions that easily. Just one question though. What does the ArrayFlatten, and the [[All, 3 ;;]] commands mean? Thank you very much for your answer.
    – wznd
    17 hours ago










  • ArrayFlatten can merge block matrices to a single matrix. And A[[All, 3 ;;]] reads off the columns 3 to Dimensions[A][[2]] of a matrix A. See the documentation of Part and Span for details.
    – Henrik Schumacher
    17 hours ago










  • Ah, now I get it. Thank you so much. If i were to calculate the change of basis matrix from W -> V, using the Inverse function, would I first take the inverse of W, and then multiply W^1 * V?
    – wznd
    17 hours ago










  • You're welcome. I'd rather use V.Inverse[W] or W.Inverse[V] depending on which direction you would like to have.
    – Henrik Schumacher
    17 hours ago










  • Well, I'd like to know the change of basis matrix from the base W -> V, so how would the function look like?
    – wznd
    16 hours ago


















  • Ah, smart. Wasn't thinking about how you could compare the two functions that easily. Just one question though. What does the ArrayFlatten, and the [[All, 3 ;;]] commands mean? Thank you very much for your answer.
    – wznd
    17 hours ago










  • ArrayFlatten can merge block matrices to a single matrix. And A[[All, 3 ;;]] reads off the columns 3 to Dimensions[A][[2]] of a matrix A. See the documentation of Part and Span for details.
    – Henrik Schumacher
    17 hours ago










  • Ah, now I get it. Thank you so much. If i were to calculate the change of basis matrix from W -> V, using the Inverse function, would I first take the inverse of W, and then multiply W^1 * V?
    – wznd
    17 hours ago










  • You're welcome. I'd rather use V.Inverse[W] or W.Inverse[V] depending on which direction you would like to have.
    – Henrik Schumacher
    17 hours ago










  • Well, I'd like to know the change of basis matrix from the base W -> V, so how would the function look like?
    – wznd
    16 hours ago
















Ah, smart. Wasn't thinking about how you could compare the two functions that easily. Just one question though. What does the ArrayFlatten, and the [[All, 3 ;;]] commands mean? Thank you very much for your answer.
– wznd
17 hours ago




Ah, smart. Wasn't thinking about how you could compare the two functions that easily. Just one question though. What does the ArrayFlatten, and the [[All, 3 ;;]] commands mean? Thank you very much for your answer.
– wznd
17 hours ago












ArrayFlatten can merge block matrices to a single matrix. And A[[All, 3 ;;]] reads off the columns 3 to Dimensions[A][[2]] of a matrix A. See the documentation of Part and Span for details.
– Henrik Schumacher
17 hours ago




ArrayFlatten can merge block matrices to a single matrix. And A[[All, 3 ;;]] reads off the columns 3 to Dimensions[A][[2]] of a matrix A. See the documentation of Part and Span for details.
– Henrik Schumacher
17 hours ago












Ah, now I get it. Thank you so much. If i were to calculate the change of basis matrix from W -> V, using the Inverse function, would I first take the inverse of W, and then multiply W^1 * V?
– wznd
17 hours ago




Ah, now I get it. Thank you so much. If i were to calculate the change of basis matrix from W -> V, using the Inverse function, would I first take the inverse of W, and then multiply W^1 * V?
– wznd
17 hours ago












You're welcome. I'd rather use V.Inverse[W] or W.Inverse[V] depending on which direction you would like to have.
– Henrik Schumacher
17 hours ago




You're welcome. I'd rather use V.Inverse[W] or W.Inverse[V] depending on which direction you would like to have.
– Henrik Schumacher
17 hours ago












Well, I'd like to know the change of basis matrix from the base W -> V, so how would the function look like?
– wznd
16 hours ago




Well, I'd like to know the change of basis matrix from the base W -> V, so how would the function look like?
– wznd
16 hours ago


















draft saved

draft discarded




















































Thanks for contributing an answer to Mathematica 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.





Some of your past answers have not been well-received, and you're in danger of being blocked from answering.


Please pay close attention to the following guidance:


  • 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.


To learn more, see our tips on writing great answers.




draft saved


draft discarded














StackExchange.ready(
function () {
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmathematica.stackexchange.com%2fquestions%2f188455%2fchange-of-basis-in-mathematica%23new-answer', 'question_page');
}
);

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







-

Popular posts from this blog

Morgemoulin

Image
Morgemoulin — miejscowość i gmina — Państwo   Francja Region Grand Est Departament Moza Okręg Verdun Kod INSEE 55357 Powierzchnia 6,82 km² Populacja  (1990) • liczba ludności 75 • gęstość 11 os./km² Kod pocztowy 55400 Położenie na mapie Francji Morgemoulin 49°14′N   5°35′E / 49,233333   5,583333 Portal Francja Morgemoulin – miejscowość i gmina we Francji, w regionie Grand Est, w departamencie Moza. Według danych na rok 1990 gminę zamieszkiwało 75 osób, a gęstość zaludnienia wynosiła 11 osób/km² (wśród 2335 gmin Lotaryngii Morgemoulin plasuje się na 970. miejscu pod względem liczby ludności, natomiast pod względem powierzchni na miejscu 848.). Bibliografia | Francuski urząd statystyczny ( fr. ) . p   •   d   •   e Gminy okręgu Verdun Abaucourt-Hautecourt • Aincreville • Ambly-sur-Meuse • Amel-sur-l'Étang • Ancemont • Arrancy-sur-Crusne • Aubréville • Autré...
Read more

Scott Moir

Image
Scott Moir Tessa Virtue i Scott Moir w 2016 r. Reprezentacja   Kanada Data i miejsce urodzenia 2 września 1987 London Wzrost 180 cm Konkurencja Pary taneczne Partner sportowy Tessa Virtue Trener Marie-France Dubreuil, Patrice Lauzon, Romain Haguenauer Poprzednio: Marina Zujewa, Oleg Epstein, Igor Szpilband, Johnny Johns, Carol Moir, Paul MacIntosh, Suzanne Killing Klub Montreal International School of Skating Poprzednio: Arctic Edge FSC Ilderton Skating Club Lokalizacja treningowa Montreal Poprzednio: Canton Kitchener Rekordy życiowe ISU przed sezonem 2018/2019 Nota łączna 206,07 Igrzyska Olimpijskie 2018 Taniec krótki 83,67 Igrzyska Olimpijskie 2018 Taniec dowolny 122,40 Igrzyska Olimpijskie 2018 Dorobek medalowy Reprezentacja   Kanada Igrzyska olimpijskie Złoto Vancouver 2010 pary taneczne Złoto Pjongczang 2018 pary taneczne Złoto Pjongczang 2018 drużynowo Srebro S...
Read more

Souastre

Image
Souastre — miejscowość i gmina — Herb Państwo   Francja Region Hauts-de-France Departament Pas-de-Calais Okręg Arras Kod INSEE 62800 Powierzchnia 7,18 km² Populacja  (1990) • liczba ludności 352 • gęstość 49 os./km² Kod pocztowy 62111 Położenie na mapie Francji Souastre 50°09′N   2°34′E / 50,150000   2,566667 Portal Francja Souastre – miejscowość i gmina we Francji, w regionie Hauts-de-France, w departamencie Pas-de-Calais. Według danych na rok 1990 gminę zamieszkiwały 352 osoby, a gęstość zaludnienia wynosiła 49 osób/km² (wśród 1549 gmin regionu Nord-Pas-de-Calais Souastre plasuje się na 887. miejscu pod względem liczby ludności, natomiast pod względem powierzchni na miejscu 507.). Bibliografia | Francuski urząd statystyczny ( fr. ) . p   •   d   •   e Gminy okręgu Arras Ablain-Saint-Nazaire Ablainzevelle Acheville Achicourt Achiet-le-Grand Achiet-le-Pe...
Read more