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Lagrangian and Hamiltonian Dynamics$
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Peter Mann

Print publication date: 2018

Print ISBN-13: 9780198822370

Published to Oxford Scholarship Online: August 2018

DOI: 10.1093/oso/9780198822370.001.0001

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The (Not So?) Basics

The (Not So?) Basics

(p.397) 30 The (Not So?) Basics
Lagrangian and Hamiltonian Dynamics

Peter Mann

Oxford University Press

This chapter discusses matrices. Matrices appear in many instances across physics, and it is in this chapter that the background necessary for understanding how to use them in calculations is provided. Although matrices can be a little daunting upon first exposure, they are very handy for a lot of classical physics. This chapter reviews the basics of matrices and their operations. It discusses square matrices, adjoint matrices, cofactor matrices and skew-symmetric matrices. The concepts of matrix multiplication, transpose, inverse, diagonal, identity, Pfaffian and determinant are examined. The chapter also discusses the terms Hermitian, symmetric and antisymmetric, as well as the Levi-Civita symbol and Laplace expansion.

Keywords:   matrix, square matrix, matrix multiplication, transpose, inverse, adjoint matrix, Hermitian, symmetric, antisymmetric, diagonal

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