Topics in Quaternion Linear Algebta

Quaternions are a number system that has become increasingly useful for representing the rotations of objects in three-dimensional space and has important applications in theoretical and applied mathematics, physics, computer science, and engineering.

The past few decades have witnessed an increasing interest in the field of multidimensional systems theory. This is concerned with systems whose trajectories depend not on one single variable (usually interpreted as time or frequency), but on several independent variables, such as the coordinates of an image.

Integer solutions for systems of linear inequalities, equations, and congruences are considered along with the construction and theoretical analysis of integer programming algorithms. The complexity of algorithms is analyzed dependent upon two parameters: the dimension, and the maximal modulus of the coefficients describing the conditions of the problem.