{|class="wikitable" align="right" style="text-align:center" |+Split-quaternion multiplication |- !width=15| × !width=15| 1 !width=15| i !width=15| j !width=15| k |- ! 1 | 1 | i | j | k |- !i |i |−1 |k |−j |- !j |j |−k |1 |−i |- !k |k |j |i |1 |}
{|class="wikitable" align="right" style="text-align:center" |+Split-quaternion multiplication |- !width=15| × !width=15| 1 !width=15| i !width=15| j !width=15| k |- ! 1 | 1 | i | j | k |- !i |i |−1 |k |−j |- !j |j |−k |1 |−i |- !k |k |j |i |1 |}
In abstract algebra, the split-quaternions or coquaternions form an algebraic structure introduced by James Cockle in 1849 under the latter name. They form an associative algebra of dimension four over the real numbers.
Discovered by embedding cosine similarity (sentence-transformers MiniLM, 384-dim).