Solvability of New Constrained Quaternion Matrix Approximation Problems Based on Core-EP Inverses
Solvability of New Constrained Quaternion Matrix Approximation Problems Based on Core-EP Inverses
复制标题
DOI：
10.1007/s00006-020-01102-7
复制
发表时间：
2020-11
影响因子：
1.5
通讯作者：
Ivan Kyrchei;D. Mosić;P. Stanimirović
中科院分区：
文献类型：
--
作者：
Ivan Kyrchei;D. Mosić;P. Stanimirović
基于核-EP逆及其对偶的性质，研究了Frobenius范数下一种新的四元数矩阵（Q-矩阵）逼近问题的三种变形：对的右列空间和的左行空间施加约束.所考虑的Q-矩阵问题的唯一解表示为的核心逆和/或的对偶核心-EP逆。因此，我们提出并解决了问题，推广了一个著名的约束逼近问题的复杂矩阵的指数为一个四元数矩阵与任意指数。给出了约束四元数矩阵逼近问题解的行列式表示。最后给出了一个例子来验证理论结果。
Based on the properties of the core-EP inverse and its dual, we investigate three variants of a novel quaternion-matrix (Q-matrix) approximation problem in the Frobenius norm:subject to the constraints imposed to the right column space ofand the left row space of. Unique solution to the considered Q-matrix problem is expressed in terms of the core inverse ofand/or the dual core-EP inverse of. Thus, we propose and solve problems which generalize a well-known constrained approximation problem for complex matrices with index one to quaternion matrices with arbitrary index. Determinantal representations for solutions of proposed constrained quaternion matrix approximation problems obtained. An example is given to justify obtained theoretical results.