The crossmetric tensor and the geometrical meaning of the imaginary numbers

The product of two Cartesian quaternions can be written as a quadratic form based on a 4x4 matrix made of the symbols 1,i,j,k where i,j,k are imaginary numbers introduced by Hamilton.

The product of two Cartesian quaternions can be written as a quadratic form based on a 4x4 matrix made of the symbols 1,i,j,k where i,j,k are imaginary numbers introduced by Hamilton. We generalized this matrix to non-Cartesian bases, and showed that the matrix is made of the…