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 the matrix algebra by extending scalars (=tensoring with a field extension), i.e. for a suitable field extension K of F, $A \otimes_F K$ is isomorphic to the 2×2 matrix algebra over K.

单词	Quaternion algebra
释义	Quaternion algebra 英语百科 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 the matrix algebra by extending scalars (=tensoring with a field extension), i.e. for a suitable field extension K of F, $A \otimes_F K$ is isomorphic to the 2×2 matrix algebra over K.
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