
We associate to every symmetric (antisymmetric) Hermitian form a system of quadratic forms over the base field which determines its isotropy and metabolicity behaviour. It is shown that two even Hermitian forms are isometric if and only if their associated systems are equivalent. As an application, it is also shown that an anisotropic symmetric Hermitian form over a quaternion division algebra in characteristic two remains anisotropic over all odd degree extensions of the ground field.
Springer's theorem, Bilinear and Hermitian forms, Hermitian form, system of quadratic forms, division algebra with involution, Quadratic forms over general fields
Springer's theorem, Bilinear and Hermitian forms, Hermitian form, system of quadratic forms, division algebra with involution, Quadratic forms over general fields
| selected citations These citations are derived from selected sources. This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically). | 6 | |
| popularity This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network. | Average | |
| influence This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically). | Top 10% | |
| impulse This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network. | Top 10% |
