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Matrices, Mappings, and Crystallographic Symmetry

Hans Wondratschek
Institut für Kristallographie, Universität Karlsruhe, Germany

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• Preface
  • List of symbols
  
  Part I. Points, vectors, and matrices
  
  
• Points and vectors
  • Points and their coordinates
  • Special coordinate systems: Cartesian coordinates
  • Vectors
  • Vector coefficients
  • The scalar product and special bases
  • Distances and angles
  
  
• Matrices and determinants
  • Mappings and symmetry operations
  • Motivation
  • The matrix formalism
  • Rules for matrix calculations
  • Determinants
  • Applications
    • Inversion of a matrix
    • Distances and angles
    • The volume of the unit cell
  
  Part II. Crystallographic applications
  
  
• Crystallographic symmetry
  • Isometries
  • Crystallographic site-symmetry operations
  • Space-group operations
  • Crystallographic groups
  • Display of crystallographic symmetry in IT A
  
  
• The description of mappings by matrix-column pairs
  • Matrix-column pairs
  • Combination and reversion of mappings
  • ($4 \times 4$) matrices
  • Transformation of vector coefficients
  • The matrix-column pairs of crystallographic symmetry operations
  • The `General Position' in IT A
  
  
• Special aspects of the matrix formalism
  • Determination of the matrix-column pair
  • The geometric meaning of (W,w)
  • Coordinate transformations
    • Origin shift
    • Change of basis
    • General coordinate transformations
  
  
• Solution of the exercises
  • Solution of problem 1
  • Solution of problem 2
  • Solution of problem 3
  
  
• .
• Index

Copyright © 2002 International Union of Crystallography