An introduction to pseudo-linear algebra

An Introduction to Pseudo-Linear Algebra

Pseudo-linear algebra is the study of common properties of linear differential and difference operators. We introduce in this paper its basic objects (pseudo-derivations, skew polynomials, and pseudo-linear operators) and describe several recent algorithms on them, which, when applied in the differential and difference cases, yield algorithms for uncoupling and solving systems of linear differe...

An Introduction To Linear Algebra

An Introduction to Linear Algebra

Introduction to Non-linear Algebra

Concise introduction to a relatively new subject of non-linear algebra: literal extension of textbook linear algebra to the case of non-linear equations and maps. This powerful science is based on the notions of discriminant (hyperdeterminant) and resultant, which today can be effectively studied both analytically and by modern computer facilities. The paper is mostly focused on resultants of n...

A brief introduction to quaternion matrices and linear algebra and on bounded groups of quaternion matrices

The division algebra of real quaternions, as the only noncommutative normed division real algebra up to isomorphism of normed algebras, is of great importance. In this note, first we present a brief introduction to quaternion matrices and quaternion linear algebra. This, among other things, will help us present the counterpart of a theorem of Herman Auerbach in the setting of quaternions. More ...