real world applications of direct sumsBook about applied linear algebra to the 3D world?What are some...
Vocabulary for giving just numbers, not a full answer
weren't playing vs didn't play
Virginia employer terminated employee and wants signing bonus returned
'The literal of type int is out of range' con número enteros pequeños (2 dígitos)
Does the nature of the Apocalypse in The Umbrella Academy change from the first to the last episode?
Could you please stop shuffling the deck and play already?
Was Luke Skywalker the leader of the Rebel forces on Hoth?
They call me Inspector Morse
Am I not good enough for you?
Why doesn't this Google Translate ad use the word "Translation" instead of "Translate"?
Should I tell my boss the work he did was worthless
How to write ı (i without dot) character in pgf-pie
meaning and function of 幸 in "则幸分我一杯羹"
Find longest word in a string: are any of these algorithms good?
Can one live in the U.S. and not use a credit card?
How did Alan Turing break the enigma code using the hint given by the lady in the bar?
How to secure an aircraft at a transient parking space?
PTIJ: wiping amalek’s memory?
Reverse string, can I make it faster?
Filtering SOQL results with optional conditionals
Are tamper resistant receptacles really safer?
Plausibility of Mushroom Buildings
Can I pump my MTB tire to max (55 psi / 380 kPa) without the tube inside bursting?
How many characters using PHB rules does it take to be able to have access to any PHB spell at the start of an adventuring day?
real world applications of direct sums
Book about applied linear algebra to the 3D world?What are some applications of Trigonometry?Surprising applications of cohomologySpace is direct sum of subspaces - propostion conditions giving me problemsApplications of Linear Algebra in software engineering.Why is matrix multiplication useful?Applications of valuation ringsExamples of non-commutative rings in natureAre there any Applications of Abstract Algebra in Engineering?History and connecting math to real world
$begingroup$
I understand how direct sums work and how they can be useful in proving certain conditional statements in linear algebra but it seems to me that direct sums are only useful in abstract settings. I was wondering if there are any real world applications for direct sums and if so, is there anywhere where I can read more about those applications since I was having trouble finding any.
linear-algebra applications direct-sum
asked 2 days ago
Gabriel ChavezGabriel Chavez
114
New contributor
Gabriel Chavez is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
$endgroup$
add a comment |
$begingroup$
I understand how direct sums work and how they can be useful in proving certain conditional statements in linear algebra but it seems to me that direct sums are only useful in abstract settings. I was wondering if there are any real world applications for direct sums and if so, is there anywhere where I can read more about those applications since I was having trouble finding any.
linear-algebra applications direct-sum
asked 2 days ago
Gabriel ChavezGabriel Chavez
114
New contributor
Gabriel Chavez is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
$endgroup$
$begingroup$
It would be impossible to construct any simple example of 2D or higher dimensional vector space without direct sum. Is this a good enough (purely mathematical) reason to consider direct sum?
$endgroup$
– edm
2 days ago
$begingroup$
hmmm... I didn't consider that. So then creating a 4d puzzle game like Miegakure (miegakure.com/) would be impossible without use of direct sums. That's cool!
$endgroup$
– Gabriel Chavez
2 days ago
$begingroup$
I mean, $Bbb R^2$ is constructed as $Bbb RoplusBbb R$, $Bbb R^3$ is constructed as $Bbb RoplusBbb RoplusBbb R$, and so on. It is not like higher dimensions are not possible, but is that we could not demonstrate their existence if we restrict the tools we use. And by the tools, I mean direct sum.
$endgroup$
– edm
2 days ago
$begingroup$
I see. thanks for the clarification.
$endgroup$
– Gabriel Chavez
2 days ago
$begingroup$
How about block matrices? A 2x2 block matrix represents an operator $A: V_1 oplus V_2 to W_1 oplus W_2$, with each block representing some component $A_{ij}: V_j to W_i$. Any time you see a block matrix, there is a direct sum behind the scenes.
$endgroup$
– Joppy
2 days ago
add a comment |
$begingroup$
I understand how direct sums work and how they can be useful in proving certain conditional statements in linear algebra but it seems to me that direct sums are only useful in abstract settings. I was wondering if there are any real world applications for direct sums and if so, is there anywhere where I can read more about those applications since I was having trouble finding any.
linear-algebra applications direct-sum
asked 2 days ago
Gabriel ChavezGabriel Chavez
114
New contributor
Gabriel Chavez is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
$endgroup$
I understand how direct sums work and how they can be useful in proving certain conditional statements in linear algebra but it seems to me that direct sums are only useful in abstract settings. I was wondering if there are any real world applications for direct sums and if so, is there anywhere where I can read more about those applications since I was having trouble finding any.
linear-algebra applications direct-sum
linear-algebra applications direct-sum
asked 2 days ago
Gabriel ChavezGabriel Chavez
114
New contributor
Gabriel Chavez is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
asked 2 days ago
Gabriel ChavezGabriel Chavez
114
New contributor
Gabriel Chavez is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
asked 2 days ago
Gabriel ChavezGabriel Chavez
114
New contributor
Gabriel Chavez is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
asked 2 days ago
Gabriel ChavezGabriel Chavez
114
asked 2 days ago
Gabriel ChavezGabriel Chavez
114
114
New contributor
Gabriel Chavez is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
New contributor
Gabriel Chavez is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
Gabriel Chavez is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
$begingroup$
It would be impossible to construct any simple example of 2D or higher dimensional vector space without direct sum. Is this a good enough (purely mathematical) reason to consider direct sum?
$endgroup$
– edm
2 days ago
$begingroup$
hmmm... I didn't consider that. So then creating a 4d puzzle game like Miegakure (miegakure.com/) would be impossible without use of direct sums. That's cool!
$endgroup$
– Gabriel Chavez
2 days ago
$begingroup$
I mean, $Bbb R^2$ is constructed as $Bbb RoplusBbb R$, $Bbb R^3$ is constructed as $Bbb RoplusBbb RoplusBbb R$, and so on. It is not like higher dimensions are not possible, but is that we could not demonstrate their existence if we restrict the tools we use. And by the tools, I mean direct sum.
$endgroup$
– edm
2 days ago
$begingroup$
I see. thanks for the clarification.
$endgroup$
– Gabriel Chavez
2 days ago
$begingroup$
How about block matrices? A 2x2 block matrix represents an operator $A: V_1 oplus V_2 to W_1 oplus W_2$, with each block representing some component $A_{ij}: V_j to W_i$. Any time you see a block matrix, there is a direct sum behind the scenes.
$endgroup$
– Joppy
2 days ago
add a comment |
$begingroup$
It would be impossible to construct any simple example of 2D or higher dimensional vector space without direct sum. Is this a good enough (purely mathematical) reason to consider direct sum?
$endgroup$
– edm
2 days ago
$begingroup$
hmmm... I didn't consider that. So then creating a 4d puzzle game like Miegakure (miegakure.com/) would be impossible without use of direct sums. That's cool!
$endgroup$
– Gabriel Chavez
2 days ago
$begingroup$
I mean, $Bbb R^2$ is constructed as $Bbb RoplusBbb R$, $Bbb R^3$ is constructed as $Bbb RoplusBbb RoplusBbb R$, and so on. It is not like higher dimensions are not possible, but is that we could not demonstrate their existence if we restrict the tools we use. And by the tools, I mean direct sum.
$endgroup$
– edm
2 days ago
$begingroup$
I see. thanks for the clarification.
$endgroup$
– Gabriel Chavez
2 days ago
$begingroup$
How about block matrices? A 2x2 block matrix represents an operator $A: V_1 oplus V_2 to W_1 oplus W_2$, with each block representing some component $A_{ij}: V_j to W_i$. Any time you see a block matrix, there is a direct sum behind the scenes.
$endgroup$
– Joppy
2 days ago
$begingroup$
It would be impossible to construct any simple example of 2D or higher dimensional vector space without direct sum. Is this a good enough (purely mathematical) reason to consider direct sum?
$endgroup$
– edm
2 days ago
$begingroup$
It would be impossible to construct any simple example of 2D or higher dimensional vector space without direct sum. Is this a good enough (purely mathematical) reason to consider direct sum?
$endgroup$
– edm
2 days ago
$begingroup$
hmmm... I didn't consider that. So then creating a 4d puzzle game like Miegakure (miegakure.com/) would be impossible without use of direct sums. That's cool!
$endgroup$
– Gabriel Chavez
2 days ago
$begingroup$
hmmm... I didn't consider that. So then creating a 4d puzzle game like Miegakure (miegakure.com/) would be impossible without use of direct sums. That's cool!
$endgroup$
– Gabriel Chavez
2 days ago
$begingroup$
I mean, $Bbb R^2$ is constructed as $Bbb RoplusBbb R$, $Bbb R^3$ is constructed as $Bbb RoplusBbb RoplusBbb R$, and so on. It is not like higher dimensions are not possible, but is that we could not demonstrate their existence if we restrict the tools we use. And by the tools, I mean direct sum.
$endgroup$
– edm
2 days ago
$begingroup$
I mean, $Bbb R^2$ is constructed as $Bbb RoplusBbb R$, $Bbb R^3$ is constructed as $Bbb RoplusBbb RoplusBbb R$, and so on. It is not like higher dimensions are not possible, but is that we could not demonstrate their existence if we restrict the tools we use. And by the tools, I mean direct sum.
$endgroup$
– edm
2 days ago
$begingroup$
I see. thanks for the clarification.
$endgroup$
– Gabriel Chavez
2 days ago
$begingroup$
I see. thanks for the clarification.
$endgroup$
– Gabriel Chavez
2 days ago
$begingroup$
How about block matrices? A 2x2 block matrix represents an operator $A: V_1 oplus V_2 to W_1 oplus W_2$, with each block representing some component $A_{ij}: V_j to W_i$. Any time you see a block matrix, there is a direct sum behind the scenes.
$endgroup$
– Joppy
2 days ago
$begingroup$
How about block matrices? A 2x2 block matrix represents an operator $A: V_1 oplus V_2 to W_1 oplus W_2$, with each block representing some component $A_{ij}: V_j to W_i$. Any time you see a block matrix, there is a direct sum behind the scenes.
$endgroup$
– Joppy
2 days ago
add a comment |
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
});
}
});
Gabriel Chavez is a new contributor. Be nice, and check out our Code of Conduct.
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%2f3140854%2freal-world-applications-of-direct-sums%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
Gabriel Chavez is a new contributor. Be nice, and check out our Code of Conduct.
Gabriel Chavez is a new contributor. Be nice, and check out our Code of Conduct.
Gabriel Chavez is a new contributor. Be nice, and check out our Code of Conduct.
Gabriel Chavez is a new contributor. Be nice, and check out our Code of Conduct.
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%2f3140854%2freal-world-applications-of-direct-sums%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
$begingroup$
It would be impossible to construct any simple example of 2D or higher dimensional vector space without direct sum. Is this a good enough (purely mathematical) reason to consider direct sum?
$endgroup$
– edm
2 days ago
$begingroup$
hmmm... I didn't consider that. So then creating a 4d puzzle game like Miegakure (miegakure.com/) would be impossible without use of direct sums. That's cool!
$endgroup$
– Gabriel Chavez
2 days ago
$begingroup$
I mean, $Bbb R^2$ is constructed as $Bbb RoplusBbb R$, $Bbb R^3$ is constructed as $Bbb RoplusBbb RoplusBbb R$, and so on. It is not like higher dimensions are not possible, but is that we could not demonstrate their existence if we restrict the tools we use. And by the tools, I mean direct sum.
$endgroup$
– edm
2 days ago
$begingroup$
I see. thanks for the clarification.
$endgroup$
– Gabriel Chavez
2 days ago
$begingroup$
How about block matrices? A 2x2 block matrix represents an operator $A: V_1 oplus V_2 to W_1 oplus W_2$, with each block representing some component $A_{ij}: V_j to W_i$. Any time you see a block matrix, there is a direct sum behind the scenes.
$endgroup$
– Joppy
2 days ago