An Algorithm for Multiplication of Two Biquaternions

In this paper we introduce efficient algorithm for the multiplication of biquaternions. The direct multiplication of two biquaternions requires 64 real multiplications and 56 real additions. More effective solutions still do not exist.We show how to compute a product of the Pauli numbers with 24 real multiplications and 64 real additions. During synthesis of the discussed algorithm we use the fact that product of two biquaternions may be represented as vector-matrix product. The matrix that participates in the product calculating has unique structural properties that allow performing its advantageous decomposition. Namely this decomposition leads to significant reducing of the computational complexity of biquaternion multiplication