This paper characterizes a class of regular para-Hermitian transfer matrices and then reveals the elementary characteristics of J -spectral factorization for this class. A transfer matrix in this class admits a J -spectral factorization if and only if there exists a common nonsingular matrix to similarly transform the A-matrices of and −1, resp., into 2 × 2 lower (upper, resp.) triangular block...

Matrices with the structures of Toeplitz, Hankel, Vandermonde and Cauchy types are omnipresent in modern computations in Sciences, Engineering and Signal and Image Processing. The four matrix classes have distinct features, but in [P90] we showed that Vandermonde and Hankel multipliers transform all these structures into each other and proposed to employ this property in order to extend any suc...

A formula is given for the propagation of errors during matrix inversion. An explicit calculation for a 2 × 2 matrix using both the formula and a Monte Carlo calculation are compared. A prescription is given to determine when a matrix with uncertain elements is sufficiently nonsingular for the calculation of the covariances of the inverted matrix elements to be reliable.

A formula for the inverse of any nonsingular matrix partitioned into two-by-two blocks is derived through a decomposition of the matrix itself and generalized inverses of the submatrices in the matrix. The formula is then applied to three matrix inverse completion problems to obtain their complete solutions.

Matrices with the structures of Toeplitz, Hankel, Vandermonde and Cauchy types are omnipresent in modern computations in Sciences, Engineering and Signal and Image Processing. The four matrix classes have distinct features, but in [P90] we showed that Vandermonde and Hankel multipliers transform all these structures into each other and proposed to employ this property in order to extend any suc...

This paper presents a new construction of matrices with no singular square submatrix. This construction allows designing erasure codes over finite fied with fast encoding and decoding algorithms. 1 Systematic MDS Erasure Codes It is well known that a [n, k, d]-error correcting code is Maximum Distance Separable (MDS) if and only if its k × n-generator matrix does not contain any singular k×k-sq...

In Communication theory and Coding, it is expected that certain circulant matrices having k ones + 1 zeros in the first row are nonsingular. We prove such always nonsingular when 2 either a power of prime, or product two distinct primes. For any other integer we construct determinant 0. The smallest singular matrix appears = 45 . possibility for to be rather low, smaller than 10 − 4 this case.

The paper mainly discusses the lower bounds for the rank of matrices and sufficient conditions for nonsingular matrices. We first present a new estimation for [Formula: see text] ([Formula: see text] is an eigenvalue of a matrix) by using the partitioned matrices. By using this estimation and inequality theory, the new and more accurate estimations for the lower bounds for the rank are deduced....

A twoperson non-zero-sum bimatrix game (A, B) is defined to be completely mixed if every solution gives a positive probability to each pure strategy of each player. Such a game is defined to be nonsingular if both payoff matrices are nonsingular. Suppose that A is perturbed to A + aG and B is perturbed to B + aH, where C and H are matrices of the same size as A and B, and OL is a small real num...