Bilinear form with parameter [closed]

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I have a bilinear form such that the associate matrix is $ A=left(beginmatrix0&0&k\
0&k&0\
k&0&0\
endmatrixright)$.
$,$ Does exist a $k$ such that $F_k((e_1+e_2+e_3),(e_1+e_2+e_3))=4$

I don't understand how can I start!

linear-algebra matrices bilinear-form

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edited Jul 16 at 16:10

Ivo Terek

43.9k949134

asked Jul 16 at 15:59

Roberto De La Fuente

417

closed as off-topic by Travis, Strants, José Carlos Santos, Adrian Keister, user223391 Jul 20 at 1:33

This question appears to be off-topic. The users who voted to close gave this specific reason:

• "This question is missing context or other details: Please improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. This information helps others identify where you have difficulties and helps them write answers appropriate to your experience level." – Travis, Strants, José Carlos Santos, Adrian Keister, Community

If this question can be reworded to fit the rules in the help center, please edit the question.

• 
  
  
  

  
  

  
  
  
  
  
  

  
  How is $F_k$ defined?
  – José Carlos Santos
  Jul 16 at 16:05
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $xz'+yy'+zx'$ right?
  – Roberto De La Fuente
  Jul 16 at 16:07
  

  
  
  
  

add a comment | 

up vote
0
down vote

favorite

I have a bilinear form such that the associate matrix is $ A=left(beginmatrix0&0&k\
0&k&0\
k&0&0\
endmatrixright)$.
$,$ Does exist a $k$ such that $F_k((e_1+e_2+e_3),(e_1+e_2+e_3))=4$

I don't understand how can I start!

linear-algebra matrices bilinear-form

share|cite|improve this question

edited Jul 16 at 16:10

Ivo Terek

43.9k949134

asked Jul 16 at 15:59

Roberto De La Fuente

417

closed as off-topic by Travis, Strants, José Carlos Santos, Adrian Keister, user223391 Jul 20 at 1:33

This question appears to be off-topic. The users who voted to close gave this specific reason:

• "This question is missing context or other details: Please improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. This information helps others identify where you have difficulties and helps them write answers appropriate to your experience level." – Travis, Strants, José Carlos Santos, Adrian Keister, Community

If this question can be reworded to fit the rules in the help center, please edit the question.

• 
  
  
  

  
  

  
  
  
  
  
  

  
  How is $F_k$ defined?
  – José Carlos Santos
  Jul 16 at 16:05
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $xz'+yy'+zx'$ right?
  – Roberto De La Fuente
  Jul 16 at 16:07
  

  
  
  
  

add a comment | 

up vote
0
down vote

favorite

up vote
0
down vote

favorite

I have a bilinear form such that the associate matrix is $ A=left(beginmatrix0&0&k\
0&k&0\
k&0&0\
endmatrixright)$.
$,$ Does exist a $k$ such that $F_k((e_1+e_2+e_3),(e_1+e_2+e_3))=4$

I don't understand how can I start!

linear-algebra matrices bilinear-form

share|cite|improve this question

edited Jul 16 at 16:10

Ivo Terek

43.9k949134

asked Jul 16 at 15:59

Roberto De La Fuente

417

I have a bilinear form such that the associate matrix is $ A=left(beginmatrix0&0&k\
0&k&0\
k&0&0\
endmatrixright)$.
$,$ Does exist a $k$ such that $F_k((e_1+e_2+e_3),(e_1+e_2+e_3))=4$

I don't understand how can I start!

linear-algebra matrices bilinear-form

share|cite|improve this question

edited Jul 16 at 16:10

Ivo Terek

43.9k949134

asked Jul 16 at 15:59

Roberto De La Fuente

417

share|cite|improve this question

share|cite|improve this question

edited Jul 16 at 16:10

Ivo Terek

43.9k949134

edited Jul 16 at 16:10

Ivo Terek

43.9k949134

edited Jul 16 at 16:10

Ivo Terek

43.9k949134

43.9k949134

asked Jul 16 at 15:59

Roberto De La Fuente

417

asked Jul 16 at 15:59

Roberto De La Fuente

417

asked Jul 16 at 15:59

Roberto De La Fuente

417

417

closed as off-topic by Travis, Strants, José Carlos Santos, Adrian Keister, user223391 Jul 20 at 1:33

This question appears to be off-topic. The users who voted to close gave this specific reason:

• "This question is missing context or other details: Please improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. This information helps others identify where you have difficulties and helps them write answers appropriate to your experience level." – Travis, Strants, José Carlos Santos, Adrian Keister, Community

If this question can be reworded to fit the rules in the help center, please edit the question.

closed as off-topic by Travis, Strants, José Carlos Santos, Adrian Keister, user223391 Jul 20 at 1:33

This question appears to be off-topic. The users who voted to close gave this specific reason:

• "This question is missing context or other details: Please improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. This information helps others identify where you have difficulties and helps them write answers appropriate to your experience level." – Travis, Strants, José Carlos Santos, Adrian Keister, Community

If this question can be reworded to fit the rules in the help center, please edit the question.

• 
  
  
  

  
  

  
  
  
  
  
  

  
  How is $F_k$ defined?
  – José Carlos Santos
  Jul 16 at 16:05
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $xz'+yy'+zx'$ right?
  – Roberto De La Fuente
  Jul 16 at 16:07
  

  
  
  
  

add a comment | 

• 
  
  
  

  
  

  
  
  
  
  
  

  
  How is $F_k$ defined?
  – José Carlos Santos
  Jul 16 at 16:05
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $xz'+yy'+zx'$ right?
  – Roberto De La Fuente
  Jul 16 at 16:07
  

  
  
  
  

How is $F_k$ defined?
– José Carlos Santos
Jul 16 at 16:05

How is $F_k$ defined?
– José Carlos Santos
Jul 16 at 16:05

$xz'+yy'+zx'$ right?
– Roberto De La Fuente
Jul 16 at 16:07

$xz'+yy'+zx'$ right?
– Roberto De La Fuente
Jul 16 at 16:07

add a comment | 

1 Answer
1

active

oldest

votes

up vote
1
down vote



accepted

You have that $F_k(vecx,vecy) = vecx^top A vecy$, so $$beginalign F_k((1,1,1),(1,1,1)) &= beginpmatrix 1 & 1 & 1endpmatrix beginpmatrix 0 & 0 & k \ 0 & k & 0 \ k & 0 & 0endpmatrix beginpmatrix 1 \ 1 \ 1 endpmatrix \ &= beginpmatrix 1 & 1 & 1endpmatrix beginpmatrix k \ k \ k endpmatrix \ &= 3kendalign$$So $k = 4/3$ fits the bill.

share|cite|improve this answer

answered Jul 16 at 16:09

Ivo Terek

43.9k949134

add a comment | 

1 Answer
1

active

oldest

votes

1 Answer
1

active

oldest

votes

active

oldest

votes

active

oldest

votes

up vote
1
down vote



accepted

You have that $F_k(vecx,vecy) = vecx^top A vecy$, so $$beginalign F_k((1,1,1),(1,1,1)) &= beginpmatrix 1 & 1 & 1endpmatrix beginpmatrix 0 & 0 & k \ 0 & k & 0 \ k & 0 & 0endpmatrix beginpmatrix 1 \ 1 \ 1 endpmatrix \ &= beginpmatrix 1 & 1 & 1endpmatrix beginpmatrix k \ k \ k endpmatrix \ &= 3kendalign$$So $k = 4/3$ fits the bill.

share|cite|improve this answer

answered Jul 16 at 16:09

Ivo Terek

43.9k949134

add a comment | 

up vote
1
down vote



accepted

You have that $F_k(vecx,vecy) = vecx^top A vecy$, so $$beginalign F_k((1,1,1),(1,1,1)) &= beginpmatrix 1 & 1 & 1endpmatrix beginpmatrix 0 & 0 & k \ 0 & k & 0 \ k & 0 & 0endpmatrix beginpmatrix 1 \ 1 \ 1 endpmatrix \ &= beginpmatrix 1 & 1 & 1endpmatrix beginpmatrix k \ k \ k endpmatrix \ &= 3kendalign$$So $k = 4/3$ fits the bill.

share|cite|improve this answer

answered Jul 16 at 16:09

Ivo Terek

43.9k949134

add a comment | 

up vote
1
down vote



accepted

up vote
1
down vote



accepted

You have that $F_k(vecx,vecy) = vecx^top A vecy$, so $$beginalign F_k((1,1,1),(1,1,1)) &= beginpmatrix 1 & 1 & 1endpmatrix beginpmatrix 0 & 0 & k \ 0 & k & 0 \ k & 0 & 0endpmatrix beginpmatrix 1 \ 1 \ 1 endpmatrix \ &= beginpmatrix 1 & 1 & 1endpmatrix beginpmatrix k \ k \ k endpmatrix \ &= 3kendalign$$So $k = 4/3$ fits the bill.

share|cite|improve this answer

answered Jul 16 at 16:09

Ivo Terek

43.9k949134

You have that $F_k(vecx,vecy) = vecx^top A vecy$, so $$beginalign F_k((1,1,1),(1,1,1)) &= beginpmatrix 1 & 1 & 1endpmatrix beginpmatrix 0 & 0 & k \ 0 & k & 0 \ k & 0 & 0endpmatrix beginpmatrix 1 \ 1 \ 1 endpmatrix \ &= beginpmatrix 1 & 1 & 1endpmatrix beginpmatrix k \ k \ k endpmatrix \ &= 3kendalign$$So $k = 4/3$ fits the bill.

share|cite|improve this answer

answered Jul 16 at 16:09

Ivo Terek

43.9k949134

share|cite|improve this answer

share|cite|improve this answer

answered Jul 16 at 16:09

Ivo Terek

43.9k949134

answered Jul 16 at 16:09

Ivo Terek

43.9k949134

answered Jul 16 at 16:09

Ivo Terek

43.9k949134

43.9k949134

add a comment | 

add a comment |