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Analytical Mechanics for Relativity and Quantum Mechanics$
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Oliver Johns

Print publication date: 2011

Print ISBN-13: 9780191001628

Published to Oxford Scholarship Online: December 2013

DOI: 10.1093/acprof:oso/9780191001628.001.0001

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Linear Operators and Dyadics

Linear Operators and Dyadics

Chapter:
(p.125) 7 Linear Operators and Dyadics
Source:
Analytical Mechanics for Relativity and Quantum Mechanics
Author(s):

Oliver Davis Johns

Publisher:
Oxford University Press
DOI:10.1093/acprof:oso/9780191001628.003.0007

This chapter introduces the concept of linear vector functions of vectors and the related dyadic notation, a concept that is particularly important in the study of rigid body motion and the covariant formulations of relativistic mechanics. Linear vector functions of vectors have a rich structure, with up to nine independent parameters needed to characterise them, and vector outputs that need not even have the same directions as the vector inputs. The subject of linear vector operators merits a chapter to itself, not only for its importance in analytical mechanics, but also because study of it will help the reader to master the operator formalism of quantum mechanics. The chapter begins with a definition of operators and matrices, and concludes with the Dirac Notation, used by quantum mechanics for complex vectors.

Keywords:   linear vector functions, vectors, dyadic notation, rigid body motion, covariant formulations, relativistic mechanics

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