Monomial (1,0,-1) - Matrices - (4×4)

The monograph "Monomial (1,0,-1)-matrices-(4×4)" is dedicated to the further development of matrix calculation in the sphere of quaternionic matrices. Mathematical description of transfer (displacement) and turn (rotation) in space are fundamental for the mechanics of rigid body. The transfer (displacement) in space is described by the vector (hodograph). The turn (rotation) in space is described by quaternion. The first part of this monograph - Application to the transfer in space - is dedicated to establish the system of basic matrices isomorphic to the quaternionic groups; to explore the qualities and structure of quaternionic matrices` multiplicative compositions; to find the equivalent correspondences to associative products of quaternionic matrices and vector algebra multiplicative compositions; to represent complex vector and scalar vector algebra products; to represent complex vector and scalar vector algebra products with quaternionic matrices. The authors consider the exposed data to be able to contribute to this research area, to permit to enhance the intellectual performance, to provide the engineer with simple and efficient mathematical apparatus.

Autorentext

Prof., Dr.-ing. Victor Kravets, PhD Tamila Kravets, National Mining University, Dnipro, Ukraine. Olexiy Burov, Jack Baskin School of Engineering, University of California-Santa Cruz, CA, USA.

Klappentext

The monograph "Monomial (1,0,-1)-matrices-(4×4)" is dedicated to the further development of matrix calculation in the sphere of quaternionic matrices. Mathematical description of transfer (displacement) and turn (rotation) in space are fundamental for the mechanics of rigid body. The transfer (displacement) in space is described by the vector (hodograph). The turn (rotation) in space is described by quaternion. The first part of this monograph - Application to the transfer in space - is dedicated to establish the system of basic matrices isomorphic to the quaternionic groups; to explore the qualities and structure of quaternionic matrices` multiplicative compositions; to find the equivalent correspondences to associative products of quaternionic matrices and vector algebra multiplicative compositions; to represent complex vector and scalar vector algebra products; to represent complex vector and scalar vector algebra products with quaternionic matrices. The authors consider the exposed data to be able to contribute to this research area, to permit to enhance the intellectual performance, to provide the engineer with simple and efficient mathematical apparatus.