Find basis from coordinates?












0












$begingroup$


Is it possible to find the basis of coordinates, in respect to the vector that led to the coordinates?



If I had a point



begin{align*} P = begin{pmatrix}
px\
py
end{pmatrix} end{align*}



and a vector



begin{align*} V = begin{pmatrix}
vx\
vy
end{pmatrix} end{align*}



, then what is the Basis B={b1,b2}?










share|cite|improve this question











$endgroup$












  • $begingroup$
    Please use Mathjax to write math expressions.
    $endgroup$
    – harshit54
    Jan 4 at 11:58












  • $begingroup$
    There wasn't really much to use Mathjax for, but here you go
    $endgroup$
    – reign
    Jan 4 at 12:16










  • $begingroup$
    There’s still more formatting to do. Be that as it may, what is the relationship between $V$ and $P$? What does $V$ have to do with this basis that you’re trying to find?
    $endgroup$
    – amd
    Jan 4 at 20:00
















0












$begingroup$


Is it possible to find the basis of coordinates, in respect to the vector that led to the coordinates?



If I had a point



begin{align*} P = begin{pmatrix}
px\
py
end{pmatrix} end{align*}



and a vector



begin{align*} V = begin{pmatrix}
vx\
vy
end{pmatrix} end{align*}



, then what is the Basis B={b1,b2}?










share|cite|improve this question











$endgroup$












  • $begingroup$
    Please use Mathjax to write math expressions.
    $endgroup$
    – harshit54
    Jan 4 at 11:58












  • $begingroup$
    There wasn't really much to use Mathjax for, but here you go
    $endgroup$
    – reign
    Jan 4 at 12:16










  • $begingroup$
    There’s still more formatting to do. Be that as it may, what is the relationship between $V$ and $P$? What does $V$ have to do with this basis that you’re trying to find?
    $endgroup$
    – amd
    Jan 4 at 20:00














0












0








0





$begingroup$


Is it possible to find the basis of coordinates, in respect to the vector that led to the coordinates?



If I had a point



begin{align*} P = begin{pmatrix}
px\
py
end{pmatrix} end{align*}



and a vector



begin{align*} V = begin{pmatrix}
vx\
vy
end{pmatrix} end{align*}



, then what is the Basis B={b1,b2}?










share|cite|improve this question











$endgroup$




Is it possible to find the basis of coordinates, in respect to the vector that led to the coordinates?



If I had a point



begin{align*} P = begin{pmatrix}
px\
py
end{pmatrix} end{align*}



and a vector



begin{align*} V = begin{pmatrix}
vx\
vy
end{pmatrix} end{align*}



, then what is the Basis B={b1,b2}?







linear-algebra






share|cite|improve this question















share|cite|improve this question













share|cite|improve this question




share|cite|improve this question








edited Jan 4 at 12:16







reign

















asked Jan 4 at 11:45









reignreign

11




11












  • $begingroup$
    Please use Mathjax to write math expressions.
    $endgroup$
    – harshit54
    Jan 4 at 11:58












  • $begingroup$
    There wasn't really much to use Mathjax for, but here you go
    $endgroup$
    – reign
    Jan 4 at 12:16










  • $begingroup$
    There’s still more formatting to do. Be that as it may, what is the relationship between $V$ and $P$? What does $V$ have to do with this basis that you’re trying to find?
    $endgroup$
    – amd
    Jan 4 at 20:00


















  • $begingroup$
    Please use Mathjax to write math expressions.
    $endgroup$
    – harshit54
    Jan 4 at 11:58












  • $begingroup$
    There wasn't really much to use Mathjax for, but here you go
    $endgroup$
    – reign
    Jan 4 at 12:16










  • $begingroup$
    There’s still more formatting to do. Be that as it may, what is the relationship between $V$ and $P$? What does $V$ have to do with this basis that you’re trying to find?
    $endgroup$
    – amd
    Jan 4 at 20:00
















$begingroup$
Please use Mathjax to write math expressions.
$endgroup$
– harshit54
Jan 4 at 11:58






$begingroup$
Please use Mathjax to write math expressions.
$endgroup$
– harshit54
Jan 4 at 11:58














$begingroup$
There wasn't really much to use Mathjax for, but here you go
$endgroup$
– reign
Jan 4 at 12:16




$begingroup$
There wasn't really much to use Mathjax for, but here you go
$endgroup$
– reign
Jan 4 at 12:16












$begingroup$
There’s still more formatting to do. Be that as it may, what is the relationship between $V$ and $P$? What does $V$ have to do with this basis that you’re trying to find?
$endgroup$
– amd
Jan 4 at 20:00




$begingroup$
There’s still more formatting to do. Be that as it may, what is the relationship between $V$ and $P$? What does $V$ have to do with this basis that you’re trying to find?
$endgroup$
– amd
Jan 4 at 20:00










0






active

oldest

votes











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
});


}
});














draft saved

draft discarded


















StackExchange.ready(
function () {
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmath.stackexchange.com%2fquestions%2f3061563%2ffind-basis-from-coordinates%23new-answer', 'question_page');
}
);

Post as a guest















Required, but never shown

























0






active

oldest

votes








0






active

oldest

votes









active

oldest

votes






active

oldest

votes
















draft saved

draft discarded




















































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.




draft saved


draft discarded














StackExchange.ready(
function () {
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmath.stackexchange.com%2fquestions%2f3061563%2ffind-basis-from-coordinates%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

Human spaceflight

Can not write log (Is /dev/pts mounted?) - openpty in Ubuntu-on-Windows?

張江高科駅