论文标题
某些四元张量系统的可溶性条件和精确溶液
The solvability conditions and exact solutions to some quaternion tensor systems
论文作者
论文摘要
我们为存在Sylvester型Quaternion Tensor System $的精确解决方案提供了必要和充分的条件 \ Mathcal {a} _i \ ast_ {n} \ Mathcal {X} _i+ \ Mathcal {Y} _i \ ast_ {M} \ Mathcal {B} \ Mathcal {z} _i \ ast_ {m} \ Mathcal {d} _i+\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ _i \ ast_ {n} \ Mathcal {z} _ {Z} _ {i+1} \ ast_} \ ast_} \ ast_} \ ast_} {m} {m} i = \覆盖{1,3} $ 使用Moore-Penrose倒数，并在可溶解后对系统的一般解决方案表示表达。作为该系统的应用，我们为Sylvester型Quaternion Tensor System $提供了可辨别性条件和一般解决方案$ \ Mathcal {a} _i \ ast_ {n} \ Mathcal {z} _i \ ast_ {m} \ Mathcal {B} _i++ \ Mathcal {C} _i \ ast_ {n} \ Mathcal {Z} _ {i+1} \ AST_ {M} \ Mathcal {d} _i = \ Mathcal {E} $ 本文还可以作为一些已知结果的扩展。
We derive necessary and sufficient conditions for the existence of the exact solution to the Sylvester-type quaternion tensor system $ \mathcal{A}_i\ast_{N}\mathcal{X}_i+ \mathcal{Y}_i\ast_{M}\mathcal{B}_i+\mathcal{C}_i\ast_{N} \mathcal{Z}_i\ast_{M}\mathcal{D}_i+\mathcal{F}_i\ast_{N} \mathcal{Z}_{i+1}\ast_{M}\mathcal{G}_i=\mathcal{E}_i, i=\overline{1,3} $ using Moore-Penrose inverse, and present an expression of the general solution to the system when it is solvable. As an application of this system, we provide the solvability conditions and general solutions for the Sylvester-type quaternion tensor system $ \mathcal{A}_i\ast_{N}\mathcal{Z}_i\ast_{M}\mathcal{B}_i+ \mathcal{C}_i\ast_{N}\mathcal{Z}_{i+1}\ast_{M}\mathcal{D}_i= \mathcal{E}_i, i=\overline{1,4}. $ This paper can also serve as extensions to some known results.
