Efficient Complex Matrix Multiplication

A well-known algorithm for complex multiplication which requires three real multiplications and five real additions is observed not to require commutativity. This extends its applicability to complex matrices, as examined in this paper. The computational savings are shown to approach 1/4, even if a real multiplication is not more computationally costly than a real addition. The computational cost function used is based on the number of equivalent real additions, with every real multiplication counted as equivalent to r real additions.