Representation of two by two matrices over perfect fields by a diagonal quadratic form

preprint2020arXivOpen access

Let F be a perfect field. Then the diagonal quadratic form $a_iX_i^2$ over $F$ is universal over $M_2(F)$ if and only if atleast two of the $a_i$ are non-zero.

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Representation of two by two matrices over perfect fields by a diagonal quadratic form

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