 Let "A" = ("a"1,"a"2) and "B" = ("b"1,"b"2) be quaternion algebras over "F".The Albert form for "A", "B" is

It can be regarded as the difference in the Witt ring of the ternary forms attached to the imaginary subspaces of "A" and "B".The quaternion algebras are linked if and only if the Albert form is isotropic, otherwise unlinked.