Cramer rule over quaternion skew field

On the Siegel-weil Formula for Quaternionic Unitary Groups

We extend the Siegel-Weil formula to all quaternion dual pairs. Applications include the classification problem of skew hermitian forms over a quaternion algebra over a number field and a product formula for the weighted average of the representation numbers of a skew hermitian form by another skew hermitian form.

Affine circle geometry over quaternion skew fields

We investigate the affine circle geometry arising from a quaternion skew field and one of its maximal commutative subfields.

Characterization of the W-weighted Drazin inverse over the quaternion skew field with applications

Codes over Quaternion Integers with Respect to Lipschitz Metric

In this paper, we study codes over some finite skew fields by using quaternion integers. Also, we obtain the decoding procedure of these codes. AMS Classification: 94B05, 94B15, 94B35, 94B60

Ela Characterization of the W-weighted Drazin Inverse over the Quaternion Skew Field with Applications

If k = 1, then X is called the group inverse of A, and is denoted by X = Ag. The Drazin inverse is very useful in various applications (see, e.g. [1]–[4]; applications in singular differential and difference equations, Markov chains and iterative methods). In 1980, Cline and Greville [5] extended the Drazin inverse of square matrix to rectangular matrix, which can be generalized to the quaterni...