The symbolic Turiyam matrix is a whose entries contain Turiyam. Inverse matrices can generally be determined if the non-singular square matrix. Currently inverse of size m × n with 6= by Moore-Penrose inverse. purpose this research to determine algorithm on real n. Algebraic operations method used obtain applying algebraic concept inverses. main result obtained demonstration example given shows...

In this paper a representation is given for the Drazin inverse of a 2 × 2 operator matrix, extending to Banach spaces results of Hartwig, Li and Wei [SIAM J. Matrix Anal. Appl., 27 (2006) pp. 757–771]. Also, formulae are derived for the Drazin inverse of an operator matrix M under some new conditions.

In this paper, we present recursive formulas for the sequential determination of the generalized LM-inverse of a general matrix. The formulas are developed for a matrix augmented by a column. These formulas are particularized to obtain also recursive relations for the generalized L-inverse of a general matrix augmented by a column.

In this paper a representation is given for the Drazin inverse of a 2 × 2 operator matrix, extending to Banach spaces results of Hartwig, Li and Wei [SIAM J. Matrix Anal. Appl., 27 (2006) pp. 757–771]. Also, formulae are derived for the Drazin inverse of an operator matrix M under some new conditions.

analysis of time series data can involve the inversion of large covariance matrices. for theclass of arma (p, q) processes there are no exact explicit expressions for these inverses, except for thema (1) process. in practice, the sample covariance matrix can be very large and inversion can becomputationally time consuming and so approximate explicit expressions for the inverse are desirable.thi...

A simple formula for the group inverse of a 2× 2 block matrix with a bipartite digraph is given in terms of the block matrices. This formula is used to give a graph-theoretic description of the group inverse of an irreducible tridiagonal matrix of odd order with zero diagonal (which is singular). Relations between the zero/nonzero structures of the group inverse and the Moore-Penrose inverse of...

An exact formula of the inverse covariance matrix of an autoregressive stochastic process is obtained using the Gohberg}Semencul explicit inverse of the Toeplitz matrix. This formula is used to build an estimator of the inverse covariance matrix of a stochastic process based on a single realization. In this paper, we show that this estimator can be conveniently applied to maximum likelihood par...

In this paper, we have developed a block cipher by using the modular arithmetic inverse of a key matrix. The key matrix is generated by taking the key in the form of twenty-eight numbers, wherein each number is represented in terms of seven binary bits. The encryption is carried out by using the key matrix containing binary bits. The decryption is performed by using the modular arithmetic inver...

For finite dimensional CMV matrices the classical inverse spectral problems are considered. We solve the inverse problem of reconstructing a CMV matrix by its Weyl’s function, the problem of reconstructing the matrix by two spectra of CMV operators with different “boundary conditions”, and the problem of reconstructing a CMV matrix by its spectrum and the spectrum of the CMV matrix obtained fro...