In abstract algebra, the biquaternions are the numbers w + x i + y j + z k, where w, x, y, and z are complex numbers, or variants thereof, and the elements...

In mathematics, a split-biquaternion is a hypercomplex number of the form q = w + x i + y j + z k , {\displaystyle q=w+x\mathrm {i} +y\mathrm {j} +z\mathrm...

In mathematics, a biquaternion algebra is a compound of quaternion algebras over a field. The biquaternions of William Rowan Hamilton (1844) and the related...

Waerden called the structure "Study biquaternions", one of three eight-dimensional algebras referred to as biquaternions. In order to describe operations...

integers. A classical example of an algebra over its center is the split-biquaternion algebra, which is isomorphic to H × H {\displaystyle \mathbb {H} \times...

effect Thomas precession Ladder paradox Twin paradox Terrell rotation Spacetime Light cone World line Minkowski diagram Biquaternions Minkowski space...

effect Thomas precession Ladder paradox Twin paradox Terrell rotation Spacetime Light cone World line Minkowski diagram Biquaternions Minkowski space...

which included presentation of biquaternions. The following passage from page 673 shows how Hamilton uses biquaternion algebra and vectors from quaternions...

involution to begin the Cayley–Dickson constructions leading to bicomplex, biquaternion, and bioctonion composition algebras. On complex numbers, the square...

quaternions C ⊗ H {\displaystyle \mathbb {C} \otimes \mathbb {H} } , or "biquaternions," are an eight-dimensional algebra dating to William Rowan Hamilton's...