The quadratic form associated to the trace form TrR^mathbf C:mathbf Ctimesmathbf CtoR, (x,y)mapstoTr(lambdaXY), where lambdaXY:mathbf Ctomathbf C is the R-linear map defined by lambdaXY(z)=xyz, is:

Q49Section II (Mathematics)49 of 190

The trace form for $\mathbb{C}/\mathbb{R}$ reduces to $2\mathrm{Re}(z^2)$

The quadratic form associated to the trace form $\mathrm{Tr}_\mathbb{R}^{\mathbf C}:\mathbf C\times\mathbf C\to\mathbb{R}$ , $(x,y)\mapsto\mathrm{Tr}(\lambda_{XY})$ , where $\lambda_{XY}:\mathbf C\to\mathbf C$ is the $\mathbb{R}$ -linear map defined by $\lambda_{XY}(z)=xyz$ , is:

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