Tessarine

Categories: Algebra stubs | Matrices | Quaternions

The tessarines are a mathematical idea introduced by James Cockle in 1848. The concept includes both ordinary complex numbers and split-complex numbers. A tessarine t may be described as a 2 × 2 complex matrix

<math>\begin{pmatrix} w & z \\ z & w\end{pmatrix}</math>.

When w and z are both real numbers, then t amounts to a split-complex number. The particular tessarine

<math>\begin{pmatrix} 0 & 1 \\ 1 & 0\end{pmatrix}</math>

has the property that its matrix product square is the identity matrix. This property lead Cockle to call the tessarine a "new imaginary in algebra". The significance of the commutative and associative ring of all tessarines seems to have been less than the significance of this particular tessarine and the plane it generates beyond the real line.