Suppose $g$ is a symmetric bilinear form, is $operatornamerad g = operatornamerad(g+g^T)$? Announcing the arrival of Valued Associate #679: Cesar Manara Planned maintenance scheduled April 23, 2019 at 00:00UTC (8:00pm US/Eastern)bilinear form decompositionSymmetric $mathbb F_2$-bilinear formBilinear form with symmetric “perpendicular” relation is either symmetric or skew-symmetricSymmetric bilinear form that is not diagonalizableSymmetric non-degerate bilinear form BSkew-symmetric non-degenerate bilinear form and $J^2=-I$ operatorSymmetric, Antisymmetric, and Alternating Bilinearforms form a vector subspaceProve that every bilinear map can be written as a sum of bilinear symmetric map and a bilinear anti-symmetric map.Proof of symmetric bilinear form and orthogonal basisBilinear form in a direct sum ex

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Suppose $g$ is a symmetric bilinear form, is $operatornamerad g = operatornamerad(g+g^T)$?



Announcing the arrival of Valued Associate #679: Cesar Manara
Planned maintenance scheduled April 23, 2019 at 00:00UTC (8:00pm US/Eastern)bilinear form decompositionSymmetric $mathbb F_2$-bilinear formBilinear form with symmetric “perpendicular” relation is either symmetric or skew-symmetricSymmetric bilinear form that is not diagonalizableSymmetric non-degerate bilinear form BSkew-symmetric non-degenerate bilinear form and $J^2=-I$ operatorSymmetric, Antisymmetric, and Alternating Bilinearforms form a vector subspaceProve that every bilinear map can be written as a sum of bilinear symmetric map and a bilinear anti-symmetric map.Proof of symmetric bilinear form and orthogonal basisBilinear form in a direct sum ex










0












$begingroup$


Is it true that, when we have a field $K$ with $operatornamechar(K) ne 2$, that $operatornamerad g = operatornamerad(g+g^T)$?



I know that in such a field, a bilinear form can be written as the sum of a symmetric and an alternating bilinear form.



How do I use this fact to prove the given statement?



Thanks.










share|cite|improve this question









$endgroup$











  • $begingroup$
    what is rad?...
    $endgroup$
    – daw
    Mar 27 at 20:35










  • $begingroup$
    @daw the radical
    $endgroup$
    – Zachary
    Mar 28 at 15:11










  • $begingroup$
    If $g$ is symmetric this is trivial since $g=g^T$, isn't it?
    $endgroup$
    – daw
    Mar 28 at 15:16










  • $begingroup$
    So rad$g$=rad$(2g$)?
    $endgroup$
    – Zachary
    Mar 28 at 15:22















0












$begingroup$


Is it true that, when we have a field $K$ with $operatornamechar(K) ne 2$, that $operatornamerad g = operatornamerad(g+g^T)$?



I know that in such a field, a bilinear form can be written as the sum of a symmetric and an alternating bilinear form.



How do I use this fact to prove the given statement?



Thanks.










share|cite|improve this question









$endgroup$











  • $begingroup$
    what is rad?...
    $endgroup$
    – daw
    Mar 27 at 20:35










  • $begingroup$
    @daw the radical
    $endgroup$
    – Zachary
    Mar 28 at 15:11










  • $begingroup$
    If $g$ is symmetric this is trivial since $g=g^T$, isn't it?
    $endgroup$
    – daw
    Mar 28 at 15:16










  • $begingroup$
    So rad$g$=rad$(2g$)?
    $endgroup$
    – Zachary
    Mar 28 at 15:22













0












0








0





$begingroup$


Is it true that, when we have a field $K$ with $operatornamechar(K) ne 2$, that $operatornamerad g = operatornamerad(g+g^T)$?



I know that in such a field, a bilinear form can be written as the sum of a symmetric and an alternating bilinear form.



How do I use this fact to prove the given statement?



Thanks.










share|cite|improve this question









$endgroup$




Is it true that, when we have a field $K$ with $operatornamechar(K) ne 2$, that $operatornamerad g = operatornamerad(g+g^T)$?



I know that in such a field, a bilinear form can be written as the sum of a symmetric and an alternating bilinear form.



How do I use this fact to prove the given statement?



Thanks.







linear-algebra






share|cite|improve this question













share|cite|improve this question











share|cite|improve this question




share|cite|improve this question










asked Mar 27 at 17:37









ZacharyZachary

3419




3419











  • $begingroup$
    what is rad?...
    $endgroup$
    – daw
    Mar 27 at 20:35










  • $begingroup$
    @daw the radical
    $endgroup$
    – Zachary
    Mar 28 at 15:11










  • $begingroup$
    If $g$ is symmetric this is trivial since $g=g^T$, isn't it?
    $endgroup$
    – daw
    Mar 28 at 15:16










  • $begingroup$
    So rad$g$=rad$(2g$)?
    $endgroup$
    – Zachary
    Mar 28 at 15:22
















  • $begingroup$
    what is rad?...
    $endgroup$
    – daw
    Mar 27 at 20:35










  • $begingroup$
    @daw the radical
    $endgroup$
    – Zachary
    Mar 28 at 15:11










  • $begingroup$
    If $g$ is symmetric this is trivial since $g=g^T$, isn't it?
    $endgroup$
    – daw
    Mar 28 at 15:16










  • $begingroup$
    So rad$g$=rad$(2g$)?
    $endgroup$
    – Zachary
    Mar 28 at 15:22















$begingroup$
what is rad?...
$endgroup$
– daw
Mar 27 at 20:35




$begingroup$
what is rad?...
$endgroup$
– daw
Mar 27 at 20:35












$begingroup$
@daw the radical
$endgroup$
– Zachary
Mar 28 at 15:11




$begingroup$
@daw the radical
$endgroup$
– Zachary
Mar 28 at 15:11












$begingroup$
If $g$ is symmetric this is trivial since $g=g^T$, isn't it?
$endgroup$
– daw
Mar 28 at 15:16




$begingroup$
If $g$ is symmetric this is trivial since $g=g^T$, isn't it?
$endgroup$
– daw
Mar 28 at 15:16












$begingroup$
So rad$g$=rad$(2g$)?
$endgroup$
– Zachary
Mar 28 at 15:22




$begingroup$
So rad$g$=rad$(2g$)?
$endgroup$
– Zachary
Mar 28 at 15:22










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