How to read $V^otimes n$?

Clash Royale CLAN TAG#URR8PPP

up vote
0
down vote

favorite

Let $V$ be a vector space and $n$ an integer. How to read $V^otimes n$? Could we read it as: $V$ to the power $n$? Thank you very much.

linear-algebra

share|cite|improve this question

asked Jul 16 at 18:12

LJR

6,43041646

• 
  
  
  

  
  

  
  
  
  
  
  

  
  en.wikipedia.org/wiki/Tensor_product
  – Lorenzo Quarisa
  Jul 16 at 18:17
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  It is tensor outer product raised to $n$
  – mathreadler
  Jul 16 at 19:20
  

  
  
  
  

add a comment | 

up vote
0
down vote

favorite

Let $V$ be a vector space and $n$ an integer. How to read $V^otimes n$? Could we read it as: $V$ to the power $n$? Thank you very much.

linear-algebra

share|cite|improve this question

asked Jul 16 at 18:12

LJR

6,43041646

• 
  
  
  

  
  

  
  
  
  
  
  

  
  en.wikipedia.org/wiki/Tensor_product
  – Lorenzo Quarisa
  Jul 16 at 18:17
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  It is tensor outer product raised to $n$
  – mathreadler
  Jul 16 at 19:20
  

  
  
  
  

add a comment | 

up vote
0
down vote

favorite

up vote
0
down vote

favorite

Let $V$ be a vector space and $n$ an integer. How to read $V^otimes n$? Could we read it as: $V$ to the power $n$? Thank you very much.

linear-algebra

share|cite|improve this question

asked Jul 16 at 18:12

LJR

6,43041646

Let $V$ be a vector space and $n$ an integer. How to read $V^otimes n$? Could we read it as: $V$ to the power $n$? Thank you very much.

linear-algebra

share|cite|improve this question

asked Jul 16 at 18:12

LJR

6,43041646

share|cite|improve this question

share|cite|improve this question

asked Jul 16 at 18:12

LJR

6,43041646

asked Jul 16 at 18:12

LJR

6,43041646

asked Jul 16 at 18:12

LJR

6,43041646

6,43041646

• 
  
  
  

  
  

  
  
  
  
  
  

  
  en.wikipedia.org/wiki/Tensor_product
  – Lorenzo Quarisa
  Jul 16 at 18:17
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  It is tensor outer product raised to $n$
  – mathreadler
  Jul 16 at 19:20
  

  
  
  
  

add a comment | 

• 
  
  
  

  
  

  
  
  
  
  
  

  
  en.wikipedia.org/wiki/Tensor_product
  – Lorenzo Quarisa
  Jul 16 at 18:17
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  It is tensor outer product raised to $n$
  – mathreadler
  Jul 16 at 19:20
  

  
  
  
  

en.wikipedia.org/wiki/Tensor_product
– Lorenzo Quarisa
Jul 16 at 18:17

en.wikipedia.org/wiki/Tensor_product
– Lorenzo Quarisa
Jul 16 at 18:17

It is tensor outer product raised to $n$
– mathreadler
Jul 16 at 19:20

It is tensor outer product raised to $n$
– mathreadler
Jul 16 at 19:20

add a comment | 

2 Answers
2

active

oldest

votes

up vote
2
down vote

This is the $n$-fold tensor product of $V$:

$$
Votimescdotsotimes Vqquad (n text times).
$$

share|cite|improve this answer

answered Jul 16 at 18:36

ervx

9,39531336

add a comment | 

up vote
1
down vote

You should read it as the $n$-th tensor power of $V$.

It is also written as $T^n(V)=V^otimes n:=V otimes ... otimes V$ $n$ times. The tensor algebra, $T(V):= bigoplus_n=0^inftyT^n(V)$, where $V^otimes 0:= K$, where $V$ is a vector space over $K$

share|cite|improve this answer

answered Jul 16 at 18:37

Mario 04

6013

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',
convertImagesToLinks: true,
noModals: false,
showLowRepImageUploadWarning: true,
reputationToPostImages: 10,
bindNavPrevention: true,
postfix: "",
noCode: true, onDemand: true,
discardSelector: ".discard-answer"
,immediatelyShowMarkdownHelp:true
);



);

 

draft saved

draft discarded

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

Name Email

StackExchange.ready(
function ()
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmath.stackexchange.com%2fquestions%2f2853687%2fhow-to-read-v-otimes-n%23new-answer', 'question_page');

);

Post as a guest

Name Email

2 Answers
2

active

oldest

votes

2 Answers
2

active

oldest

votes

active

oldest

votes

active

oldest

votes

up vote
2
down vote

This is the $n$-fold tensor product of $V$:

$$
Votimescdotsotimes Vqquad (n text times).
$$

share|cite|improve this answer

answered Jul 16 at 18:36

ervx

9,39531336

add a comment | 

up vote
2
down vote

This is the $n$-fold tensor product of $V$:

$$
Votimescdotsotimes Vqquad (n text times).
$$

share|cite|improve this answer

answered Jul 16 at 18:36

ervx

9,39531336

add a comment | 

up vote
2
down vote

up vote
2
down vote

This is the $n$-fold tensor product of $V$:

$$
Votimescdotsotimes Vqquad (n text times).
$$

share|cite|improve this answer

answered Jul 16 at 18:36

ervx

9,39531336

This is the $n$-fold tensor product of $V$:

$$
Votimescdotsotimes Vqquad (n text times).
$$

share|cite|improve this answer

answered Jul 16 at 18:36

ervx

9,39531336

share|cite|improve this answer

share|cite|improve this answer

answered Jul 16 at 18:36

ervx

9,39531336

answered Jul 16 at 18:36

ervx

9,39531336

answered Jul 16 at 18:36

ervx

9,39531336

9,39531336

add a comment | 

add a comment | 

up vote
1
down vote

You should read it as the $n$-th tensor power of $V$.

It is also written as $T^n(V)=V^otimes n:=V otimes ... otimes V$ $n$ times. The tensor algebra, $T(V):= bigoplus_n=0^inftyT^n(V)$, where $V^otimes 0:= K$, where $V$ is a vector space over $K$

share|cite|improve this answer

answered Jul 16 at 18:37

Mario 04

6013

add a comment | 

up vote
1
down vote

You should read it as the $n$-th tensor power of $V$.

It is also written as $T^n(V)=V^otimes n:=V otimes ... otimes V$ $n$ times. The tensor algebra, $T(V):= bigoplus_n=0^inftyT^n(V)$, where $V^otimes 0:= K$, where $V$ is a vector space over $K$

share|cite|improve this answer

answered Jul 16 at 18:37

Mario 04

6013

add a comment | 

up vote
1
down vote

up vote
1
down vote

You should read it as the $n$-th tensor power of $V$.

It is also written as $T^n(V)=V^otimes n:=V otimes ... otimes V$ $n$ times. The tensor algebra, $T(V):= bigoplus_n=0^inftyT^n(V)$, where $V^otimes 0:= K$, where $V$ is a vector space over $K$

share|cite|improve this answer

answered Jul 16 at 18:37

Mario 04

6013

You should read it as the $n$-th tensor power of $V$.

It is also written as $T^n(V)=V^otimes n:=V otimes ... otimes V$ $n$ times. The tensor algebra, $T(V):= bigoplus_n=0^inftyT^n(V)$, where $V^otimes 0:= K$, where $V$ is a vector space over $K$

share|cite|improve this answer

answered Jul 16 at 18:37

Mario 04

6013

share|cite|improve this answer

share|cite|improve this answer

answered Jul 16 at 18:37

Mario 04

6013

answered Jul 16 at 18:37

Mario 04

6013

answered Jul 16 at 18:37

Mario 04

6013

6013

add a comment | 

add a comment | 

 

draft saved

draft discarded

 

draft saved

draft discarded

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

Name Email

StackExchange.ready(
function ()
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmath.stackexchange.com%2fquestions%2f2853687%2fhow-to-read-v-otimes-n%23new-answer', 'question_page');

);

Post as a guest

Name Email

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

Name Email

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

Name Email

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

Name Email

Name Email

Name

Email

Name Email

Name

Email