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## Main Question or Discussion Point

Hello,

If I have a quadratic form ##q## on a ##\mathbb{R}## vectorial space ##E##, its associated bilinear symmetric form ##b## can be deduce by the following formula : ##b(., .) = \frac{q(. + .) - q(.) - q(.)}{2}##.

Can we generalize this at a k multilinear symmetric form?

Have a nice day.

If I have a quadratic form ##q## on a ##\mathbb{R}## vectorial space ##E##, its associated bilinear symmetric form ##b## can be deduce by the following formula : ##b(., .) = \frac{q(. + .) - q(.) - q(.)}{2}##.

**So that, an homogeneous polynomial of degree 2 can be associated to a blinear symmetric form.**Can we generalize this at a k multilinear symmetric form?

**(I mean associate to an homogeneous polynomial of degree k a k multilinear symmetric form).**Have a nice day.