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, i.e. for a suitable field extension K of F, A ⊗ F K {\displaystyle A\otimes _{F}K} is isomorphic to the 2×2 matrix algebra over K. The notion of a quaternion algebra can be seen as a generalization of Hamilton's quaternions to an arbitrary base field. Wikipedia