Linear Representation
For tessarine note that since ij = k . The mapping
is a linear representation of the algebra of tessarines as a subalgebra of 2 x 2 complex matrices. For instance, ik = i(ij) = (ii)j = −j in the linear representation is
Note that unlike most matrix algebras, this is a commutative algebra.
Read more about this topic: Bicomplex Number