Abstract
We present an efficient algorithm to multiply two arbitrary biquaternions. The schoolbook 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 biquaternions with 24 real multiplications and 56 real additions. During synthesis of the discussed algorithm we use the fact that product of two biquaternions may be represented as a matrix–vector product. The matrix multiplicand that participates in the product calculating has unique structural properties that allow performing its advantageous factorization. Namely this factorization leads to significant reducing of the computational complexity of biquaternion multiplication.
Published Version
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