Let K<sup>n×n</sup> be the set of all n×n matrices and K<sub>r</sub><sup>n×n</sup> the set {A∈K<sup>n×n</sup>|rankA=r} on askew field K. Zhuang [1] ...Let K<sup>n×n</sup> be the set of all n×n matrices and K<sub>r</sub><sup>n×n</sup> the set {A∈K<sup>n×n</sup>|rankA=r} on askew field K. Zhuang [1] denotes by A<sup>#</sup> the group inverse of A∈K<sup>n×n</sup> which is the solu-tion of the euqations:AXA=A, XAX=X, AX=AX.展开更多
In this paper we study a matrix equation AX+BX=C （Ⅰ）over an arbitrary skew field,and give a consistency criterion of （Ⅰ） and an explicit expression of general solutions of （Ⅰ）.A convenient,simple and practi...In this paper we study a matrix equation AX+BX=C （Ⅰ）over an arbitrary skew field,and give a consistency criterion of （Ⅰ） and an explicit expression of general solutions of （Ⅰ）.A convenient,simple and practical method of solving （Ⅰ） is also given.As a particular case,we also give a simple method of finding a system of fundamental solutions of a homogeneous system of right linear equations over a skew field.展开更多
在斜地 K 上认为稳定的 Steinberg 组圣是(K) 。元素 x 被称为复杂物如果 x^2 = 1。在这篇论文，复杂物被允许是身份。Theauthors 证明直到变化形式的 GL_n (K) 的元素 A 能作为 BC 被代表，在 B 更低的地方三角形并且 C 同时是上面的...在斜地 K 上认为稳定的 Steinberg 组圣是(K) 。元素 x 被称为复杂物如果 x^2 = 1。在这篇论文，复杂物被允许是身份。Theauthors 证明直到变化形式的 GL_n (K) 的元素 A 能作为 BC 被代表，在 B 更低的地方三角形并且 C 同时是上面的三角形。而且， B 和 C 能被选择以便在 B 的主要对角线的元素是β _ 1，β _ 2，吗？ ? ?，β _ n，并且照顾γ _ 1，γ _ 2，？？，γ _ n c_n c_n ∈[K~* ， K~*] 并且Π _(j=1 )~ n β _ j γ _ j = detA。在圣(K) 的每元素δ是 10 复杂物的一个产品，这也被证明。展开更多
The matrix equation A mn X ns B st =C over an arbitrary skew field is considered. A necessary and sufficient condition for the consistency and the expression for general solutions of the above mentioned matrix equatio...The matrix equation A mn X ns B st =C over an arbitrary skew field is considered. A necessary and sufficient condition for the consistency and the expression for general solutions of the above mentioned matrix equation are presented.Moreover,a practical method of solving one is also given.展开更多
基金This work is Supported by NSF of Heilongjiang Provice
文摘Let K<sup>n×n</sup> be the set of all n×n matrices and K<sub>r</sub><sup>n×n</sup> the set {A∈K<sup>n×n</sup>|rankA=r} on askew field K. Zhuang [1] denotes by A<sup>#</sup> the group inverse of A∈K<sup>n×n</sup> which is the solu-tion of the euqations:AXA=A, XAX=X, AX=AX.
文摘In this paper we study a matrix equation AX+BX=C （Ⅰ）over an arbitrary skew field,and give a consistency criterion of （Ⅰ） and an explicit expression of general solutions of （Ⅰ）.A convenient,simple and practical method of solving （Ⅰ） is also given.As a particular case,we also give a simple method of finding a system of fundamental solutions of a homogeneous system of right linear equations over a skew field.
文摘The matrix equation A mn X ns B st =C over an arbitrary skew field is considered. A necessary and sufficient condition for the consistency and the expression for general solutions of the above mentioned matrix equation are presented.Moreover,a practical method of solving one is also given.
