Signature of a quadratic form from matrix
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I have the following quadratic form :
$q(x,y,z)=x(y+4z)+y(x-2z)+x^2$. Before giving its signature, I am asked to work out its matrix, which should be $begin{bmatrix}1&1&2\1&0&-1\2&-1&0end{bmatrix}$.
This makes me wonder whether there is a way to work out its signature other than by grouping the squared linear terms.
quadratic-forms
asked Nov 14 at 10:26
James Well
511410
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I have the following quadratic form :
$q(x,y,z)=x(y+4z)+y(x-2z)+x^2$. Before giving its signature, I am asked to work out its matrix, which should be $begin{bmatrix}1&1&2\1&0&-1\2&-1&0end{bmatrix}$.
This makes me wonder whether there is a way to work out its signature other than by grouping the squared linear terms.
quadratic-forms
asked Nov 14 at 10:26
James Well
511410
Diagonalize the matrix....or at least find out exactly as possible where its eigenvalues lie, which also will help you with the other part of this question. There is one negative eigenvalue and two positive ones, so the signature is $;(2,1,0);$
– DonAntonio
Nov 14 at 10:53
add a comment |
up vote
0
down vote
favorite
up vote
0
down vote
favorite
I have the following quadratic form :
$q(x,y,z)=x(y+4z)+y(x-2z)+x^2$. Before giving its signature, I am asked to work out its matrix, which should be $begin{bmatrix}1&1&2\1&0&-1\2&-1&0end{bmatrix}$.
This makes me wonder whether there is a way to work out its signature other than by grouping the squared linear terms.
quadratic-forms
asked Nov 14 at 10:26
James Well
511410
I have the following quadratic form :
$q(x,y,z)=x(y+4z)+y(x-2z)+x^2$. Before giving its signature, I am asked to work out its matrix, which should be $begin{bmatrix}1&1&2\1&0&-1\2&-1&0end{bmatrix}$.
This makes me wonder whether there is a way to work out its signature other than by grouping the squared linear terms.
quadratic-forms
quadratic-forms
asked Nov 14 at 10:26
James Well
511410
asked Nov 14 at 10:26
James Well
511410
asked Nov 14 at 10:26
James Well
511410
asked Nov 14 at 10:26
James Well
511410
asked Nov 14 at 10:26
James Well
511410
511410
Diagonalize the matrix....or at least find out exactly as possible where its eigenvalues lie, which also will help you with the other part of this question. There is one negative eigenvalue and two positive ones, so the signature is $;(2,1,0);$
– DonAntonio
Nov 14 at 10:53
add a comment |
Diagonalize the matrix....or at least find out exactly as possible where its eigenvalues lie, which also will help you with the other part of this question. There is one negative eigenvalue and two positive ones, so the signature is $;(2,1,0);$
– DonAntonio
Nov 14 at 10:53
Diagonalize the matrix....or at least find out exactly as possible where its eigenvalues lie, which also will help you with the other part of this question. There is one negative eigenvalue and two positive ones, so the signature is $;(2,1,0);$
– DonAntonio
Nov 14 at 10:53
Diagonalize the matrix....or at least find out exactly as possible where its eigenvalues lie, which also will help you with the other part of this question. There is one negative eigenvalue and two positive ones, so the signature is $;(2,1,0);$
– DonAntonio
Nov 14 at 10:53
add a comment |
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Diagonalize the matrix....or at least find out exactly as possible where its eigenvalues lie, which also will help you with the other part of this question. There is one negative eigenvalue and two positive ones, so the signature is $;(2,1,0);$
– DonAntonio
Nov 14 at 10:53