Explicit group inverse of an innovative patterned matrix

In this paper, we present an innovative patterned matrix, RFPL-Toeplitz matrix, is neither the extension of Toeplitz matrix nor its special case. We show that the group inverse of this new patterned matrix can be represented as the sum of products of lower and upper triangular Toeplitz matrices. First, the explicit expression of the group inverse of an RFPL-Toeplitz matrix is obtained. Second, the decomposition of the group inverse is given. Finally, an example demonstrates availability of the two methods for the group inverse.