A note on generalized G-matrices

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• 作者：Masaya Matsuura ^{masaya@ehime-u.ac.jp}
• 关键词：15A09 ; 15A23 ; 15B05
• 刊名：Linear Algebra and its Applications
• 出版年：2012
• 期刊代码：38_00243795
• 类别：mt
• 出版时间：1 May, 2012
• 卷：436
• 期：9
• 页码：3475-3479
• 文件大小：212 K

摘要

In this paper, we slightly generalize the notion of G-matrices, which has been recently introduced. A real nonsingular matrix A is called a G-matrix if there exist nonsingular diagonal matrices and such that . We generalize this definition to the case where A can be singular. We say that a real matrix A, which is not necessarily square, is a generalized G-matrix (GG-matrix) if there exist nonsingular diagonal matrices and such that is a g-inverse of A. The main purpose of this paper is to show that any generalized Cauchy matrix is a GG-matrix.