Invertibility of Matrices of Field Elements

Determinant and Inverse of Matrices of Real Elements

In this paper the classic theory of matrices of real elements (see e.g. [12], [13]) is developed. We prove selected equations that have been proved previously for matrices of field elements. Similarly, we introduce in this special context the determinant of a matrix, the identity and zero matrices, and the inverse matrix. The new concept discussed in the case of matrices of real numbers is the ...

On Regularity of Incline Matrices

Abstract In this paper, we exhibit that, in an incline L, the greatest element ‘1’ is the multiplicative identity for the elements of DL, the set of idempotent elements in L. We have discussed the invertibility of matrices over DL and for matrices over an integral incline. We have obtained equivalent conditions for regularity of a matrix over an incline whose idempotent elements are linearly or...

Left invertibility of discrete-time output-quantized systems: the linear case with finite inputs

This paper studies left invertibility of discrete-time linear outputquantized systems. Quantized outputs are generated according to a given partition of the state-space, while inputs are sequences on a finite alphabet. Left invertibility, i.e. injectivity of I/O map, is reduced to left D-invertibility, under suitable conditions. While left invertibility takes into account membership to sets of ...

Verification of Invertibility of Complicated Functions over Large Domains

A new method to decide the invertibility of a given high-dimensional function over a domain is presented. The problem arises in the field of verified solution of differential algebraic equations (DAEs) related to the need to perform projections of certain constraint manifolds over large domains. The question of invertibility is reduced to a verified linear algebra problem involving first partia...

A Survey of Invertibility and Spectrum Preserving Linear Maps