相关论文: The Moore-Penrose inverses of split quaternions

The theory of matrix splitting is a useful tool for finding solution of rectangular linear system of equations, iteratively. The purpose of this paper is two-fold. Firstly, we revisit theory of weak regular splittings for rectangular…

In this paper, we introduce a ring isomorphism between the Clifford algebra $C\ell_2$ and a ring of matrices, and represent the elements in $C\ell_2$ by real matrices. By such a ring isomorphism, we introduce the concept of the…

In this paper, we derive explicit formulas for computing the roots of $ax^{2}+bx+c=0$ with $a$ being not invertible in split quaternion algebra. We also imitate the approach developed by Opfer, Janovska and Falcao etc. to verify our results…

In this paper, we introduce a ring isomorphism between the Clifford algebra $C\ell_{1,2}$ and a ring of matrices. By such a ring isomorphism, we introduce the concept of the Moore-Penrose inverse in Clifford algebra $C\ell_{1,2}$. Using the…

In this article, specific definitions of the Moore-Penrose inverse, Drazin inverse of the quaternion tensor and the inverse along two quaternion tensors are introduced under the T-product. Some characterizations, representations and…

In the last decades the Moore-Penrose pseudoinverse has found a wide range of applications in many areas of Science and became a useful tool for physicists dealing, for instance, with optimization problems, with data analysis, with the…

Determinantal representation of the Moore-Penrose inverse over the quaternion skew field is obtained within the framework of a theory of the column and row determinants. Using the obtained analogs of the adjoint matrix, we get the Cramer…

Unlike the Hamilton quaternion algebra, the split-quaternions contain nontrivial zero divisors. In general speaking, it is hard to find the solutions of equations in algebras containing zero divisor. In this paper, we manage to derive…

In this paper, the consimilarity of complex matrices is generalized for the split quaternions. In this regard, coneigenvalue and coneigenvector are defined for split quaternion matrices. Also, the existence of solution to the split…

We present explicit formulas for Moore-Penrose inverses of some families of set inclusion matrices arising from sets, vector spaces, and designs.

The Moore-Penrose inverse of a matrix has been extensively investigated and widely applied in many fields over the past decades. One reason for the interest is that the Moore-Penrose inverse can succinctly express some important geometric…

We develop quaternion--native iterative methods for computing the Moore--Penrose (MP) pseudoinverse of quaternion matrices and analyze their convergence. Our starting point is a damped Newton--Schulz (NS) iteration tailored to…

Over an algebraically closed field, we describe the affine varieties of solutions to the linear equations $a(xb)=c$ and $a(bx)=c$ over the split-octonions. We also determine the dimensions of the solution sets of arbitrary linear monomial…

We establish some relationships between an m-accretive operator and its Moore-Penorse inverse. We derive some perturbation result of the Moore-Penorse inverse of a maximal accretive operator. As an application we give a factorization…

The quaternionic equations ax-xb=0 and ax-xb=c are investigated, which are called homogeneous and inhomogeneous Sylvester equations, respectively. Conditions for the existence of solutions are provided. In addition, the general and nonzero…

Within the framework of the theory of quaternion column-row determinants and using determinantal representations of the Moore-Penrose inverse previously obtained by the author, we get explicit determinantal representation formulas of…

In this paper, real matrix representations of split quaternions are examined in terms of the casual character of quaternion. Then, we give De-Moivre' s formula for real matrices of timelike and spacelike split quaternions, separately.…

In this article we provide a fast computational method in order to calculate the Moore-Penrose inverse of singular square matrices and of rectangular matrices. The proposed method proves to be much faster and has significantly better…

We employ the M-P inverses and ranks of quaternion matrices to establish the necessary and sufficient conditions for solving a system of the dual quaternion matrix equations $(AX, XC) = (B, D)$, along with providing an expression for its…

Reverse order law for the Moore-Penrose inverses of tensors are useful in the field of multilinear algebra. In this paper, we first prove some more identities involving the Moore-Penrose inverse of tensors. We then obtain a few necessary…