Gauss sums and quadratic forms on matrices (Q2706983)
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scientific article
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Gauss sums and quadratic forms on matrices |
scientific article |
Statements
2 July 2001
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Gauss sums
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trace
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quadratic form
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quadratic space
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radicals
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canonical orthogonal splittings
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discriminants
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Gauss sums and quadratic forms on matrices (English)
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Let \(F\) be a field of characteristic different from 2 and \(M_n(F)\) the ring of \(n\times n\) matrices over \(F\). Fix \(A\in M_n(F)\) and define \(Q(X)=\text{tr}(AX^2)\) for \(X\in M_n(F)\), when tr denotes the trace of matrices. This quadratic form \(Q\) gives \(M_n(F)\) the structure of a quadratic space. The authors study the radicals, the canonical orthogonal splittings and the discriminants.
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