Characterizations and properties of the matrices A such that AA(−1)(L) -A(−1)(L) A are nonsingular

Jiabao Wu, Kezheng Zuo, Jiale Gao, Lu Zheng


In this paper, we consider the co-BD matrices, a class of matrices characterized by the invertibility of AA(−1)(L) − A(−1)(L) A, where A(−1)(L) is the Bott-Duffin inverse of A with respect to a subspace L. Different characterizations and properties of this class of matrices are given. Also, we consider some characterizations of the nonsingularity of AA(−1)(L) + A(−1)(L) A and In − A(A(−1)(L) )2A.


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