Completing a2×2Block Matrix of Real Quaternions with a Partial Specified Inverse

Completing a 2 × 2 Block Matrix of Real Quaternions with a Partial Specified

Involution Matrices of Real Quaternions

An involution or anti-involution is a self-inverse linear mapping. In this paper, we will present two real quaternion matrices, one corresponding to a real quaternion involution and one corresponding to a real quaternion anti-involution. Moreover, properties and geometrical meanings of these matrices will be given as reflections in R^3.

Inverse Kinematics using Quaternions

In this project I describe the status of inverse kinematics research, with the focus firmly on the methods that solve the core problem. An overview of the different methods are presented Three common methods used in inverse kinematics computation have been chosen as subject for closer inspection. The three methods are described in some detail. An analysis is performed where the three methods ar...

determinant of the hankel matrix with binomial entries

abstract in this thesis at first we comput the determinant of hankel matrix with enteries a_k (x)=?_(m=0)^k??((2k+2-m)¦(k-m)) x^m ? by using a new operator, ? and by writing and solving differential equation of order two at points x=2 and x=-2 . also we show that this determinant under k-binomial transformation is invariant.

Completing Inverse Entailment

Yamamoto has shown that the Inverse Entailment (IE) mechanism described previously by the author is complete for Plotkin's relative subsumption but incomplete for entailment. That is to say, an hy-pothesised clause H can be derived from an example E under a background theory B using IE if and only if H subsumes E relative to B in Plotkin's sense. Yamamoto gives examples of H for which B H j = E...