Search

In this paper, by applying particular structure of the real representations of quaternion matrices and the Moore–Penrose generalized inverse, we derive the expressions of the minimal norm least squares solution, the pure imaginary least squares solution, and the real least squares solution for the quaternion matrix equation A X = B . The resulting formulas only involve real matrices, which are simpler than those reported in (Yuan et al., 2013). The corresponding algorithms only perform real arithmetic which also consider particular structure of the real representations of quaternion matrices, therefore are very efficient and easily understood. Numerical examples are provided to illustrate the efficiency of our algorithms. [ABSTRACT FROM AUTHOR]

Abstract: In this paper we propose a fast structure-preserving algorithm for computing the singular value decomposition of quaternion matrices. The algorithm is based on the structure-preserving bidiagonalization of the real counterpart for quaternion matrices by applying orthogonal JRS-symplectic matrices. The algorithm is efficient and numerically stable. [Copyright &y& Elsevier]

Abstract: In this article we give some formulas for the maximal and minimal ranks of the submatrices in a least squares solution X to AXB = C. From these formulas, we derive necessary and sufficient conditions for the submatrices to be zero and other special forms, respectively. Finally, some Hermitian properties for least squares solution to matrix equation AXB = C are derived. [Copyright &y& Elsevier]

• The structure matrices for most finite Boolean-type lattices and complementation algebras are presented. • Using the structure matrices, the homomorphisms and isomorphisms of BTAs are investigated. • The decomposition of a BTA is considered, which means decomposing a BTA into a product of two BTAs, and a straightforward verifiable necessary and sufficient condition is obtained. This paper provides a systematic matrix description for finite Boolean- type algebras (BTAs). A BTA is decomposed into Boolean-type lattice (BTL) and a complementation algebra (CA). When the object set is finite, the matrix expressions of BTL and CA (and then of BTA) are presented. Via their matrix expression, the construction and certain properties of BTAs are investigated, including the homomorphism and isomorphism, as well as the decomposition. Moreover, straightforward verifiable conditions are obtained to detect the properties above by means of logical matrices operations. [ABSTRACT FROM AUTHOR]