The solvability of two linear matrix equations
The solvability of two linear matrix equations
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DOI：
10.1080/03081080008818664
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发表时间：
2000-12
影响因子：
1.1
通讯作者：
Yongge Tian
中科院分区：
文献类型：
--
作者：
Yongge Tian
使用矩阵的秩和广义逆来建立以下两个线性矩阵方程 (i)A1X1B1 +A2X2B2 +A3X3B3 =C,(ii) A1XB1 =C1 A2XB2 =C2 的可解性条件。另外，三类矩阵方程的对偶性 (iii) A 1 X 1 B 1+A 2 X 2 B 2+A 3 X 3 B 3+A 4 X 4 B 4=C, (iv) A 1 XB 1=C 1 A 2 XB 2=C 2 A 3 XB 3=C 3 A 4 XB 4=C 4, (v) AXB+CXD=E 也被考虑。
The solvability conditions of the following two linear matrix equations (i)A1X1B1 +A2X2B2 +A3X3B3 =C,(ii) A1XB1 =C1 A2XB2 =C2 are established using ranks and generalized inverses of matrices. In addition, the duality of the three types of matrix equations (iii) A 1 X 1 B 1+A 2 X 2 B 2+A 3 X 3 B 3+A 4 X 4 B 4=C, (iv) A 1 XB 1=C 1 A 2 XB 2=C 2 A 3 XB 3=C 3 A 4 XB 4=C 4, (v) AXB+CXD=E are also considered.