: Mathématiques: quaternion algebra

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quaternion algebra

In mathematics, a quaternion algebra over a field F is a central simple algebra A over F that has dimension 4 over F. Every quaternion algebra becomes a matrix algebra by extending scalars (equivalently, tensoring with a field extension), i.e. for a suitable field extension K of F, ${\\displaystyle A\\otimes _{F}K}$ is isomorphic to the 2 × 2 matrix algebra over K.
(Wikipedia, The Free Encyclopedia, https://en.wikipedia.org/wiki/Quaternion_algebra)

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