Quadratic Forms rank and signature confusion
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I would just like to clear some things up!
A quadratic form can always be expressed in terms of a symmetric matrix. When we diagonalise this matrix we can read the rank and signature of the quadratic form off this matrix, right?
Also, is the signature of a quadratic form always the number of positive eigenvalues minus the number of negative eigenvalues?
Many thanks!
quadratic-forms matrix-rank
asked Nov 30 '18 at 18:26
MathematicianPMathematicianP
2916
$endgroup$
add a comment |
$begingroup$
I would just like to clear some things up!
A quadratic form can always be expressed in terms of a symmetric matrix. When we diagonalise this matrix we can read the rank and signature of the quadratic form off this matrix, right?
Also, is the signature of a quadratic form always the number of positive eigenvalues minus the number of negative eigenvalues?
Many thanks!
quadratic-forms matrix-rank
asked Nov 30 '18 at 18:26
MathematicianPMathematicianP
2916
$endgroup$
add a comment |
$begingroup$
I would just like to clear some things up!
A quadratic form can always be expressed in terms of a symmetric matrix. When we diagonalise this matrix we can read the rank and signature of the quadratic form off this matrix, right?
Also, is the signature of a quadratic form always the number of positive eigenvalues minus the number of negative eigenvalues?
Many thanks!
quadratic-forms matrix-rank
asked Nov 30 '18 at 18:26
MathematicianPMathematicianP
2916
$endgroup$
I would just like to clear some things up!
A quadratic form can always be expressed in terms of a symmetric matrix. When we diagonalise this matrix we can read the rank and signature of the quadratic form off this matrix, right?
Also, is the signature of a quadratic form always the number of positive eigenvalues minus the number of negative eigenvalues?
Many thanks!
quadratic-forms matrix-rank
quadratic-forms matrix-rank
asked Nov 30 '18 at 18:26
MathematicianPMathematicianP
2916
asked Nov 30 '18 at 18:26
MathematicianPMathematicianP
2916
asked Nov 30 '18 at 18:26
MathematicianPMathematicianP
2916
asked Nov 30 '18 at 18:26
MathematicianPMathematicianP
2916
asked Nov 30 '18 at 18:26
MathematicianPMathematicianP
2916
2916
add a comment |
add a comment |
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