Biquaternion Algebra with Bilinear Multiplication: A General, Elegant, and Computationally Advantageous Framework for Relativistic Electronic Structure Calculations on CPUs and GPUs

Quaternion algebra provides a natural representation of time-reversal-symmetric matrix structures in relativistic electronic-structure theory, whereas complementary time-reversal-antisymmetric structures extend this representation to complex quaternions, or biquaternions. Here, we explicitly exploit