On the matrix equation Ax = λBx
On the matrix equation Ax = λBx
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关于矩阵方程 Ax = λBx
DOI：
10.1016/0022-247x(67)90169-2
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发表时间：
1967
影响因子：
1.3
通讯作者：
I. Erdelyi
中科院分区：
文献类型：
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作者：
I. Erdelyi
C= D-lIZTAT-1D-1/2 9 y= D112 Tx，参见例如[1，21.这种减少Eq。(I)在非奇异矩阵的领域之外，对于形式（II），可能会遇到几个限制。本文讨论了A和B都是复数域上矩形奇异矩阵的情形。根据非奇异矩阵的类比，自然可以诉诸Moore-Bjerhammar-Penrose的矩阵广义逆的概念，在Penrose的公式中，下面的定义成立：
C= D-lIZTAT-1D-l/2 9 y= D112Tx, see, for example,[l, 21. Such reductions of Eq.(I) to the form (II), beyond the field of nonsingular matrices, may encounter several limitations. We ate concerned here with the case in which A and B are both rectangular ot singular matrices over the complex field. Following the analogy of the nonsingular matrices, it is natural to appeal to Moore-Bjerhammar-Penrose’s concept of the generalized inverse1 of matrices for which the following definition, in Penrose’s formulation, holds: