ON THE MATRIX REALIZATION OF THE THEORY OF BIQUATERNIONS

This paper describes a matrix algebra realization of Clifford's theory of biquaternions. By examining 4 x 4 skew-symmetric matrices, the pap er shows the connection between infinitesimal screws in elliptic three -space and vector quaternions. By studying the matrix exponential of t he skew-symmetric matrices, the paper also shows how finite screws in elliptic three-space lead to matrix realization of quaternions. Finall y, it is shown that line transformations in elliptic three-space lead to double quaternions and that a dual quaternion is a limiting case of a double quaternion.