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

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

Rank Equalities for Moore-penrose Inverse and Drazin Inverse over Quaternion

In this paper, we consider the ranks of four real matrices Gi(i = 0, 1, 2, 3) in M†, where M = M0 +M1i+M2j+M3k is an arbitrary quaternion matrix, and M† = G0 + G1i + G2j + G3k is the Moore-Penrose inverse of M . Similarly, the ranks of four real matrices in Drazin inverse of a quaternion matrix are also presented. As applications, the necessary and sufficient conditions for M† is pure real or p...

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.

Ela Group Inverse for the Block Matrix with Two Identical Subblocks over Skew Fields

is called the Drazin inverse of A and is denoted by X = A, where k is the index of A, i.e., the smallest non-negative integer such that rank(A) = rank(A). We denote such a k by Ind(A). It is well-known that A exists and is unique (see [2]). If Ind(A) = 1, A is also called the group inverse of A and is denoted by A. Then A exists if and only if rank(A) = rank(A) (see [1, 3, 11-14, 24, 25, 29]). ...

Cramer rule over quaternion skew field

New definitions of determinant functionals over the quaternion skew field are given in this paper. The inverse matrix over the quaternion skew field is represented by analogues of the classical adjoint matrix. Cramer rule for right and left quaternionic systems of linear equations have been obtained.