… In this review we present a theory of the quasideterminants defined for matrices over a
division ring. r 2004 Elsevier Inc. All rights reserved. … In Section 2 we discuss an important …

… Then a quasideterminant of matrix X … quasideterminant of A. This principle is not valid for
commutative determinants, because they are not defined for block-matrices. Quasideterminants …

The notion of a quasideterminant and a quasiminor of a matrix A=(a_{ij}) with not necessarily
commuting entries was introduced recently by I.Gelfand and the second author. The …

… of quasideterminants for matrices over a noncommutative division ring was introduced in [GR,
GR1, GR2]. Quasideterminants … We believe that quasideterminants should be one of main …

… In fact, our Theorem 3.3 shows that any quasideterminant of A is a sum of monomials in the
… up to n2 quasideterminants of A. If A is a square matrix we call a quasideterminant of any k × …

… The aim of this article is to demonstrate that the quasi-determinants of Gelfand and
Retakh can be applied successfully to the important problem of describing the algebraic …

… these continued fractions (ie the weights of the path models) and the coefficients of their
series expansion, we will be led naturally to express results in terms of the quasi-determinants …

… properties of quasideterminants that are … of quasideterminants stated in section 2 to effect
a direct verification of the solutions described in (30). By recognizing that the quasideterminant …

… form of a product of principal quasi-determinants. In this note we … Namely, we have found a
family of quasi-determinants that … We will also introduce notations for quasi-determinants that …

We discuss an extension of soliton theory and integrable systems to noncommutative spaces,
focusing on integrable aspects of noncommutative anti-self-dual Yang–Mills equations. …